Theorem f1fn 5093

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 5092	. 2 |- ( F : A -1-1-> B -> F : A --> B )
2		ffn 5046	. 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 4897   -->wf 4898   -1-1->wf1 4899

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99

This theorem depends on definitions:  df-bi 110  df-f 4906  df-f1 4907

This theorem is referenced by:  f1fun  5094  f1rel  5095  f1dm  5096  f1ssr  5098  f1f1orn  5137  f1elima  5412  f1eqcocnv  5431  f1oiso  5465  phplem4dom  6324