Theorem f1fun 5261

Description: A one-to-one mapping is a function. (Contributed by set.mm contributors, 8-Mar-2014.)

Assertion

Ref	Expression
f1fun	|- (F:A-1-1->B -> Fun F)

Proof of Theorem f1fun

Step	Hyp	Ref	Expression
1		f1fn 5260	. 2 |- (F:A-1-1->B -> F Fn A)
2		fnfun 5182	. 2 |- (F Fn A -> Fun F)
3	1, 2	syl 15	1 |- (F:A-1-1->B -> Fun F)

This proof depends on syntax axioms:   -> wi 4  Fun wfun 4776   Fn wfn 4777  -1-1->wf1 4779

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 177  df-an 360  df-fn 4791  df-f 4792  df-f1 4793

This theorem is used by:  fun11iun  5306