Theorem f1ofn 5575

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

Assertion

Ref	Expression
f1ofn	|- ( F : A -1-1-onto-> B -> F Fn A )

Proof of Theorem f1ofn

Step	Hyp	Ref	Expression
1		f1of 5574	. 2 |- ( F : A -1-1-onto-> B -> F : A --> B )
2		ffn 5473	. 2 |- ( F : A --> B -> F Fn A )
3	1, 2	syl 14	1 |- ( F : A -1-1-onto-> B -> F Fn A )

Syntax hints:   -> wi 4   Fn wfn 5313   -->wf 5314   -1-1-onto->wf1o 5317

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-f 5322  df-f1 5323  df-f1o 5325

This theorem is referenced by:  f1ofun  5576  f1odm  5578  isocnv2  5942  isoini  5948  isoselem  5950  bren  6903  en1  6959  en2  6981  xpen  7014  phplem4  7024  phplem4on  7037  dif1en  7049  fiintim  7104  residfi  7118  supisolem  7186  ordiso2  7213  inresflem  7238  eldju  7246  caseinl  7269  caseinr  7270  enomnilem  7316  enmkvlem  7339  enwomnilem  7347  iseqf1olemnab  10735  hashfacen  11071  fprodssdc  12117  phimullem  12763  znleval  14633