Theorem f1f 5258

Description: A one-to-one mapping is a mapping. (Contributed by set.mm contributors, 31-Dec-1996.)

Assertion

Ref	Expression
f1f	|- (F:A-1-1->B -> F:A-->B)

Proof of Theorem f1f

Step	Hyp	Ref	Expression
1		df-f1 4792	. 2 |- (F:A-1-1->B <-> (F:A-->B /\ Fun `'F))
2	1	simplbi 446	1 |- (F:A-1-1->B -> F:A-->B)

Syntax hints:   -> wi 4  `'ccnv 4771  Fun wfun 4775  -->wf 4777  -1-1->wf1 4778

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 177  df-an 360  df-f1 4792

This theorem is referenced by:  f1fn  5259  f1ss  5262  f1of  5287  dff1o5  5295  fun11iun  5305  dflec3  6221