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Theorem f1ofun 5289

Description: A one-to-one onto mapping is a function. (Contributed by set.mm contributors, 12-Dec-2003.)

**Assertion**
Ref	Expression
f1ofun	⊢ (F:A–1-1-onto→B → Fun F)

**Proof of Theorem f1ofun**
Step	Hyp	Ref	Expression
1		f1ofn 5288	. 2 ⊢ (F:A–1-1-onto→B → F Fn A)
2		fnfun 5181	. 2 ⊢ (F Fn A → Fun F)
3	1, 2	syl 15	1 ⊢ (F:A–1-1-onto→B → Fun F)

Colors of variables: wff setvar class

Syntax hints: → wi 4 Fun wfun 4775 Fn wfn 4776 –1-1-onto→wf1o 4780

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

This theorem depends on definitions: df-bi 177 df-an 360 df-fn 4790 df-f 4791 df-f1 4792 df-f1o 4794

This theorem is referenced by: f1ococnv2 5309 enpw1 6062 sbthlem3 6205