Theorem f1fn 5424

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 5422	. 2 |- ( F : A -1-1-> B -> F : A --> B )
2		ffn 5366	. 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 5212   -->wf 5213   -1-1->wf1 5214

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 5221  df-f1 5222

This theorem is referenced by:  f1fun  5425  f1rel  5426  f1dm  5427  f1ssr  5429  f1f1orn  5473  f1elima  5774  f1eqcocnv  5792  f1oiso  5827  phplem4dom  6862  f1finf1o  6946  updjudhcoinlf  7079  updjudhcoinrg  7080  updjud  7081  fihashf1rn  10768