diff --git a/Doc/lib/libitertools.tex b/Doc/lib/libitertools.tex
index df73561ceb6..be53015f7cd 100644
--- a/Doc/lib/libitertools.tex
+++ b/Doc/lib/libitertools.tex
@@ -458,15 +458,21 @@ def nth(iterable, n):
 
 def all(seq, pred=bool):
     "Returns True if pred(x) is True for every element in the iterable"
-    return False not in imap(pred, seq)
+    for elem in ifilterfalse(pred, seq):
+        return False
+    return True
 
 def any(seq, pred=bool):
-    "Returns True if pred(x) is True at least one element in the iterable"
-    return True in imap(pred, seq)
+    "Returns True if pred(x) is True for at least one element in the iterable"
+    for elem in ifilter(pred, seq):
+        return True
+    return False
 
 def no(seq, pred=bool):
     "Returns True if pred(x) is False for every element in the iterable"
-    return True not in imap(pred, seq)
+    for elem in ifilter(pred, seq):
+        return False
+    return True
 
 def quantify(seq, pred=bool):
     "Count how many times the predicate is True in the sequence"
diff --git a/Lib/test/test_itertools.py b/Lib/test/test_itertools.py
index e4c29ad33b3..6ce758a99eb 100644
--- a/Lib/test/test_itertools.py
+++ b/Lib/test/test_itertools.py
@@ -746,15 +746,21 @@ Samuele
 
 >>> def all(seq, pred=bool):
 ...     "Returns True if pred(x) is True for every element in the iterable"
-...     return False not in imap(pred, seq)
+...     for elem in ifilterfalse(pred, seq):
+...         return False
+...     return True
 
 >>> def any(seq, pred=bool):
 ...     "Returns True if pred(x) is True for at least one element in the iterable"
-...     return True in imap(pred, seq)
+...     for elem in ifilter(pred, seq):
+...         return True
+...     return False
 
 >>> def no(seq, pred=bool):
 ...     "Returns True if pred(x) is False for every element in the iterable"
-...     return True not in imap(pred, seq)
+...     for elem in ifilter(pred, seq):
+...         return False
+...     return True
 
 >>> def quantify(seq, pred=bool):
 ...     "Count how many times the predicate is True in the sequence"