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Theorem funforn 5276

Description: A function maps its domain onto its range. (Contributed by set.mm contributors, 23-Jul-2004.)

**Assertion**
Ref	Expression
funforn	⊢ (Fun A ↔ A:dom A–onto→ran A)

**Proof of Theorem funforn**
Step	Hyp	Ref	Expression
1		funfn 5136	. 2 ⊢ (Fun A ↔ A Fn dom A)
2		dffn4 5275	. 2 ⊢ (A Fn dom A ↔ A:dom A–onto→ran A)
3	1, 2	bitri 240	1 ⊢ (Fun A ↔ A:dom A–onto→ran A)

Colors of variables: wff setvar class

Syntax hints: ↔ wb 176 dom cdm 4772 ran crn 4773 Fun wfun 4775 Fn wfn 4776 –onto→wfo 4779

This theorem was proved from axioms: ax-1 5 ax-2 6 ax-3 7 ax-mp 8 ax-gen 1546 ax-ext 2334

This theorem depends on definitions: df-bi 177 df-an 360 df-cleq 2346 df-fn 4790 df-fo 4793

This theorem is referenced by: (None)