diff --git a/NEWS.md b/NEWS.md
index abb7240cc9..9df8a4c1e0 100644
--- a/NEWS.md
+++ b/NEWS.md
@@ -5,6 +5,10 @@
 
 * R >=3.6.0 is now explicitly required (#7026).
 
+* `if_any()` and `if_all()` are now fully consistent with `any()` and `all()`. 
+  In particular, when called with empty inputs `if_any()` returns `FALSE` and 
+  `if_all()` returns `TRUE` (#7059, @jrwinget).
+
 # dplyr 1.1.4
 
 * `join_by()` now allows its helper functions to be namespaced with `dplyr::`,
diff --git a/R/across.R b/R/across.R
index 8262ef6b1e..e42fe28ed5 100644
--- a/R/across.R
+++ b/R/across.R
@@ -4,7 +4,7 @@
 #' `across()` makes it easy to apply the same transformation to multiple
 #' columns, allowing you to use [select()] semantics inside in "data-masking"
 #' functions like [summarise()] and [mutate()]. See `vignette("colwise")` for
-#'  more details.
+#' more details.
 #'
 #' `if_any()` and `if_all()` apply the same
 #' predicate function to a selection of columns and combine the
@@ -18,6 +18,14 @@
 #' `across()` supersedes the family of "scoped variants" like
 #' `summarise_at()`, `summarise_if()`, and `summarise_all()`.
 #'
+#' @details
+#' When there are no selected columns:
+#'
+#' - `if_any()` will return `FALSE`, consistent with the behavior of
+#'   `any()` when called without inputs.
+#' - `if_all()` will return `TRUE`, consistent with the behavior of
+#'   `all()` when called without inputs.
+#'
 #' @param .cols <[`tidy-select`][dplyr_tidy_select]> Columns to transform.
 #'   You can't select grouping columns because they are already automatically
 #'   handled by the verb (i.e. [summarise()] or [mutate()]).
@@ -133,9 +141,16 @@
 #' iris %>%
 #'   group_by(Species) %>%
 #'   summarise(across(starts_with("Sepal"), mean, .names = "mean_{.col}"))
+#'
 #' iris %>%
 #'   group_by(Species) %>%
-#'   summarise(across(starts_with("Sepal"), list(mean = mean, sd = sd), .names = "{.col}.{.fn}"))
+#'   summarise(
+#'     across(
+#'       starts_with("Sepal"),
+#'       list(mean = mean, sd = sd),
+#'       .names = "{.col}.{.fn}"
+#'     )
+#'   )
 #'
 #' # If a named external vector is used for column selection, .names will use
 #' # those names when constructing the output names
@@ -146,7 +161,9 @@
 #' # When the list is not named, .fn is replaced by the function's position
 #' iris %>%
 #'   group_by(Species) %>%
-#'   summarise(across(starts_with("Sepal"), list(mean, sd), .names = "{.col}.fn{.fn}"))
+#'   summarise(
+#'     across(starts_with("Sepal"), list(mean, sd), .names = "{.col}.fn{.fn}")
+#'   )
 #'
 #' # When the functions in .fns return a data frame, you typically get a
 #' # "packed" data frame back
@@ -164,7 +181,9 @@
 #'
 #' # .unpack can utilize a glue specification if you don't like the defaults
 #' iris %>%
-#'   reframe(across(starts_with("Sepal"), quantile_df, .unpack = "{outer}.{inner}"))
+#'   reframe(
+#'     across(starts_with("Sepal"), quantile_df, .unpack = "{outer}.{inner}")
+#'   )
 #'
 #' # This is also useful inside mutate(), for example, with a multi-lag helper
 #' multilag <- function(x, lags = 1:3) {
@@ -618,9 +637,11 @@ expand_if_across <- function(quo) {
   if (is_call(call, "if_any")) {
     op <- "|"
     if_fn <- "if_any"
+    empty <- FALSE
   } else {
     op <- "&"
     if_fn <- "if_all"
+    empty <- TRUE
   }
 
   context_local("across_if_fn", if_fn)
@@ -634,9 +655,10 @@ expand_if_across <- function(quo) {
   call[[1]] <- quote(across)
   quos <- expand_across(quo_set_expr(quo, call))
 
-  # Select all rows if there are no inputs
+  # Select all rows if there are no inputs for if_all(),
+  # but select no rows if there are no inputs for if_any().
   if (!length(quos)) {
-    return(list(quo(TRUE)))
+    return(list(quo(!!empty)))
   }
 
   combine <- function(x, y) {
diff --git a/man/across.Rd b/man/across.Rd
index 7907d0a9dd..51afbbfc90 100644
--- a/man/across.Rd
+++ b/man/across.Rd
@@ -86,6 +86,15 @@ of them, then you probably want to use \code{\link[=pick]{pick()}} instead.
 \code{across()} supersedes the family of "scoped variants" like
 \code{summarise_at()}, \code{summarise_if()}, and \code{summarise_all()}.
 }
+\details{
+When there are no selected columns:
+\itemize{
+\item \code{if_any()} will return \code{FALSE}, consistent with the behavior of
+\code{any()} when called without inputs.
+\item \code{if_all()} will return \code{TRUE}, consistent with the behavior of
+\code{all()} when called without inputs.
+}
+}
 \section{Timing of evaluation}{
 
 R code in dplyr verbs is generally evaluated once per group.
@@ -177,9 +186,16 @@ iris \%>\%
 iris \%>\%
   group_by(Species) \%>\%
   summarise(across(starts_with("Sepal"), mean, .names = "mean_{.col}"))
+
 iris \%>\%
   group_by(Species) \%>\%
-  summarise(across(starts_with("Sepal"), list(mean = mean, sd = sd), .names = "{.col}.{.fn}"))
+  summarise(
+    across(
+      starts_with("Sepal"),
+      list(mean = mean, sd = sd),
+      .names = "{.col}.{.fn}"
+    )
+  )
 
 # If a named external vector is used for column selection, .names will use
 # those names when constructing the output names
@@ -190,7 +206,9 @@ iris \%>\%
 # When the list is not named, .fn is replaced by the function's position
 iris \%>\%
   group_by(Species) \%>\%
-  summarise(across(starts_with("Sepal"), list(mean, sd), .names = "{.col}.fn{.fn}"))
+  summarise(
+    across(starts_with("Sepal"), list(mean, sd), .names = "{.col}.fn{.fn}")
+  )
 
 # When the functions in .fns return a data frame, you typically get a
 # "packed" data frame back
@@ -208,7 +226,9 @@ iris \%>\%
 
 # .unpack can utilize a glue specification if you don't like the defaults
 iris \%>\%
-  reframe(across(starts_with("Sepal"), quantile_df, .unpack = "{outer}.{inner}"))
+  reframe(
+    across(starts_with("Sepal"), quantile_df, .unpack = "{outer}.{inner}")
+  )
 
 # This is also useful inside mutate(), for example, with a multi-lag helper
 multilag <- function(x, lags = 1:3) {
diff --git a/tests/testthat/test-across.R b/tests/testthat/test-across.R
index d2116c2c22..a23dde57ac 100644
--- a/tests/testthat/test-across.R
+++ b/tests/testthat/test-across.R
@@ -870,7 +870,7 @@ test_that("if_any() and if_all() expansions deal with no inputs or single inputs
   # No inputs
   expect_equal(
     filter(d, if_any(starts_with("c"), ~ FALSE)),
-    filter(d)
+    filter(d, FALSE)
   )
   expect_equal(
     filter(d, if_all(starts_with("c"), ~ FALSE)),
@@ -888,6 +888,32 @@ test_that("if_any() and if_all() expansions deal with no inputs or single inputs
   )
 })
 
+test_that("if_any() on zero-column selection behaves like any() (#7059)", {
+  tbl <- tibble(
+    x1 = 1:5,
+    x2 = c(-1, 4, 5, 4, 1),
+    y = c(1, 4, 2, 4, 9),
+  )
+
+  expect_equal(
+    filter(tbl, if_any(c(), ~ is.na(.x))),
+    tbl[0, ]
+  )
+})
+
+test_that("if_all() on zero-column selection behaves like all() (#7059)", {
+  tbl <- tibble(
+    x1 = 1:5,
+    x2 = c(-1, 4, 5, 4, 1),
+    y = c(1, 4, 2, 4, 9),
+  )
+
+  expect_equal(
+    filter(tbl, if_all(c(), ~ is.na(.x))),
+    tbl
+  )
+})
+
 test_that("if_any() and if_all() wrapped deal with no inputs or single inputs", {
   d <- data.frame(x = 1)