Theorem funforn 5277

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 5137	. 2 |- (Fun A <-> A Fn dom A)
2		dffn4 5276	. 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)

This proof depends on syntax axioms:   <-> wb 176  dom cdm 4773  ran crn 4774  Fun wfun 4776   Fn wfn 4777  -onto->wfo 4780

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-ext 2334

This proof depends on definitions:  df-bi 177  df-an 360  df-cleq 2346  df-fn 4791  df-fo 4794

This theorem is used by: (None)