Theorem f1f 5533

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 5323	. 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 4718   Fun wfun 5312   -->wf 5314   -1-1->wf1 5315

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 5323

This theorem is referenced by:  f1rn  5534  f1fn  5535  f1ss  5539  f1ssres  5542  f1of  5574  dff1o5  5583  fsnd  5618  cocan1  5917  f1o2ndf1  6380  brdomg  6905  f1dom2g  6915  f1domg  6917  dom3d  6933  f1imaen2g  6953  2dom  6966  dom1o  6985  xpdom2  6998  dom0  7007  phplem4dom  7031  isinfinf  7067  infm  7077  updjudhcoinlf  7258  updjudhcoinrg  7259  casef1  7268  djudom  7271  difinfsnlem  7277  difinfsn  7278  seqf1oglem1  10753  fihashf1rn  11022  ennnfonelemrn  13006  reeff1o  15463  ushgruhgr  15896  umgr0e  15934  usgredgssen  15976  ausgrusgrben  15982  usgrss  15991  uspgrupgr  15995  usgrumgr  15998  usgrislfuspgrdom  16004  ushgredgedg  16040  ushgredgedgloop  16042  1dom1el  16437  3dom  16439  pwle2  16451