Theorem f1ofun 5582

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 5581	. 2 |- ( F : A -1-1-onto-> B -> F Fn A )
2		fnfun 5424	. 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 5318   Fn wfn 5319   -1-1-onto->wf1o 5323

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 5327  df-f 5328  df-f1 5329  df-f1o 5331

This theorem is referenced by:  f1orel  5583  f1oresrab  5808  isose  5957  f1opw  6225  xpcomco  7005  fiintim  7116  f1dmvrnfibi  7134  caseinl  7281  caseinr  7282  ctssdccl  7301  ctssdclemr  7302  fihasheqf1oi  11039  fisumss  11943  ennnfonelemex  13025  ennnfonelemf1  13029  hmeontr  15027