Theorem f1fn 5325

Description: A one-to-one mapping is a function on its domain. (Contributed by NM, 8-Mar-2014.)

Assertion

Ref	Expression
f1fn	|- ( F : A -1-1-> B -> F Fn A )

Proof of Theorem f1fn

Step	Hyp	Ref	Expression
1		f1f 5323	. 2 |- ( F : A -1-1-> B -> F : A --> B )
2		ffn 5267	. 2 |- ( F : A --> B -> F Fn A )
3	1, 2	syl 14	1 |- ( F : A -1-1-> B -> F Fn A )

Syntax hints:   -> wi 4   Fn wfn 5113   -->wf 5114   -1-1->wf1 5115

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105

This theorem depends on definitions:  df-bi 116  df-f 5122  df-f1 5123

This theorem is referenced by:  f1fun  5326  f1rel  5327  f1dm  5328  f1ssr  5330  f1f1orn  5371  f1elima  5667  f1eqcocnv  5685  f1oiso  5720  phplem4dom  6749  f1finf1o  6828  updjudhcoinlf  6958  updjudhcoinrg  6959  updjud  6960  fihashf1rn  10528