Theorem funforn 5551

Description: A function maps its domain onto its range. (Contributed by NM, 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 5344	. 2 |- ( Fun A <-> A Fn dom A )
2		dffn4 5550	. 2 |- ( A Fn dom A <-> A : dom A -onto-> ran A )
3	1, 2	bitri 184	1 |- ( Fun A <-> A : dom A -onto-> ran A )

Syntax hints:   <-> wb 105   dom cdm 4716   ran crn 4717   Fun wfun 5308   Fn wfn 5309   -onto->wfo 5312

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-gen 1495  ax-ext 2211

This theorem depends on definitions:  df-bi 117  df-cleq 2222  df-fn 5317  df-fo 5320

This theorem is referenced by:  dvrecap  15372