Theorem funforn 5133

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 4951	. 2 |- ( Fun A <-> A Fn dom A )
2		dffn4 5132	. 2 |- ( A Fn dom A <-> A : dom A -onto-> ran A )
3	1, 2	bitri 182	1 |- ( Fun A <-> A : dom A -onto-> ran A )

Syntax hints:   <-> wb 103   dom cdm 4363   ran crn 4364   Fun wfun 4916   Fn wfn 4917   -onto->wfo 4920

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-gen 1378  ax-ext 2063

This theorem depends on definitions:  df-bi 115  df-cleq 2074  df-fn 4925  df-fo 4928

This theorem is referenced by: (None)