Theorem funforn 5622

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 5407	. 2 |- ( Fun A <-> A Fn dom A )
2		dffn4 5621	. 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 )

This proof depends on syntax axioms:   <-> wb 105   dom cdm 4774   ran crn 4775   Fun wfun 5371   Fn wfn 5372   -onto->wfo 5375

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-gen 1502  ax-ext 2220

This proof depends on definitions:  df-bi 117  df-cleq 2231  df-fn 5380  df-fo 5383

This theorem is used by:  imacosuppfn  6508  dvrecap  15816