Theorem f1fn 5113

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 5112	. 2 |- ( F : A -1-1-> B -> F : A --> B )
2		ffn 5066	. 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 4917   -->wf 4918   -1-1->wf1 4919

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104

This theorem depends on definitions:  df-bi 115  df-f 4926  df-f1 4927

This theorem is referenced by:  f1fun  5114  f1rel  5115  f1dm  5116  f1ssr  5118  f1f1orn  5157  f1elima  5433  f1eqcocnv  5451  f1oiso  5485  phplem4dom  6348