Theorem f1fun 5260

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 5259	. 2 ⊢ (F:A–1-1→B → F Fn A)
2		fnfun 5181	. 2 ⊢ (F Fn A → Fun F)
3	1, 2	syl 15	1 ⊢ (F:A–1-1→B → Fun F)

Syntax hints:   → wi 4  Fun wfun 4775   Fn wfn 4776  –1-1→wf1 4778

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 177  df-an 360  df-fn 4790  df-f 4791  df-f1 4792

This theorem is referenced by:  fun11iun  5305