Theorem f1f 5440

Description: A one-to-one mapping is a mapping. (Contributed by NM, 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 5240	. 2 |- ( F : A -1-1-> B <-> ( F : A --> B /\ Fun `' F ) )
2	1	simplbi 274	1 |- ( F : A -1-1-> B -> F : A --> B )

Syntax hints:   -> wi 4   `'ccnv 4643   Fun wfun 5229   -->wf 5231   -1-1->wf1 5232

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106

This theorem depends on definitions:  df-bi 117  df-f1 5240

This theorem is referenced by:  f1rn  5441  f1fn  5442  f1ss  5446  f1ssres  5449  f1of  5480  dff1o5  5489  fsnd  5523  cocan1  5809  f1o2ndf1  6254  brdomg  6775  f1dom2g  6783  f1domg  6785  dom3d  6801  f1imaen2g  6820  2dom  6832  xpdom2  6858  dom0  6867  phplem4dom  6891  isinfinf  6926  infm  6933  updjudhcoinlf  7110  updjudhcoinrg  7111  casef1  7120  djudom  7123  difinfsnlem  7129  difinfsn  7130  fihashf1rn  10803  ennnfonelemrn  12473  reeff1o  14671  1dom1el  15221  pwle2  15227