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Theorem f1ofn 5288

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

**Assertion**
Ref	Expression
f1ofn	⊢ (F:A–1-1-onto→B → F Fn A)

**Proof of Theorem f1ofn**
Step	Hyp	Ref	Expression
1		f1of 5287	. 2 ⊢ (F:A–1-1-onto→B → F:A–→B)
2		ffn 5223	. 2 ⊢ (F:A–→B → F Fn A)
3	1, 2	syl 15	1 ⊢ (F:A–1-1-onto→B → F Fn A)

Colors of variables: wff setvar class

Syntax hints: → wi 4 Fn wfn 4776 –→wf 4777 –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-f 4791 df-f1 4792 df-f1o 4794

This theorem is referenced by: f1ofun 5289 f1odm 5290 f1ofveu 5480 isomin 5496 isoini 5497 nenpw1pwlem2 6085