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Theorem f1odm 5290

Description: The domain of a one-to-one onto mapping. (Contributed by set.mm contributors, 8-Mar-2014.)

**Assertion**
Ref	Expression
f1odm	⊢ (F:A–1-1-onto→B → dom F = A)

**Proof of Theorem f1odm**
Step	Hyp	Ref	Expression
1		f1ofn 5288	. 2 ⊢ (F:A–1-1-onto→B → F Fn A)
2		fndm 5182	. 2 ⊢ (F Fn A → dom F = A)
3	1, 2	syl 15	1 ⊢ (F:A–1-1-onto→B → dom F = A)

Colors of variables: wff setvar class

Syntax hints: → wi 4 = wceq 1642 dom cdm 4772 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: bren 6030 enpw1 6062 enmap1lem5 6073 nenpw1pwlem2 6085 ncdisjun 6136 sbthlem3 6205