Theorem f1ofun 5585

Description: A one-to-one onto mapping is a function. (Contributed by NM, 12-Dec-2003.)

Assertion

Ref	Expression
f1ofun	|- ( F : A -1-1-onto-> B -> Fun F )

Proof of Theorem f1ofun

Step	Hyp	Ref	Expression
1		f1ofn 5584	. 2 |- ( F : A -1-1-onto-> B -> F Fn A )
2		fnfun 5427	. 2 |- ( F Fn A -> Fun F )
3	1, 2	syl 14	1 |- ( F : A -1-1-onto-> B -> Fun F )

Syntax hints:   -> wi 4   Fun wfun 5320   Fn wfn 5321   -1-1-onto->wf1o 5325

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-fn 5329  df-f 5330  df-f1 5331  df-f1o 5333

This theorem is referenced by:  f1orel  5586  f1oresrab  5812  isose  5961  f1opw  6229  xpcomco  7009  fiintim  7122  f1dmvrnfibi  7142  caseinl  7289  caseinr  7290  ctssdccl  7309  ctssdclemr  7310  fihasheqf1oi  11048  fisumss  11952  ennnfonelemex  13034  ennnfonelemf1  13038  hmeontr  15036