Theorem funforn 5411

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 5212	. 2 |- ( Fun A <-> A Fn dom A )
2		dffn4 5410	. 2 |- ( A Fn dom A <-> A : dom A -onto-> ran A )
3	1, 2	bitri 183	1 |- ( Fun A <-> A : dom A -onto-> ran A )

Syntax hints:   <-> wb 104   dom cdm 4598   ran crn 4599   Fun wfun 5176   Fn wfn 5177   -onto->wfo 5180

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-gen 1436  ax-ext 2146

This theorem depends on definitions:  df-bi 116  df-cleq 2157  df-fn 5185  df-fo 5188

This theorem is referenced by:  dvrecap  13218