Theorem funforn 3684

Description: A function maps its domain onto its range.

Assertion

Ref	Expression
funforn	|- (Fun A <-> A:dom A-onto->ran A)

Proof of Theorem funforn

Step	Hyp	Ref	Expression
1		funfn 3548	. 2 |- (Fun A <-> A Fn dom A)
2		fnforn 3683	. 2 |- (A Fn dom A <-> A:dom A-onto->ran A)
3	1, 2	bitr 173	1 |- (Fun A <-> A:dom A-onto->ran A)

Syntax hints:   <-> wb 146  dom cdm 3176  ran crn 3177  Fun wfun 3182   Fn wfn 3183  -onto->wfo 3186

This theorem is referenced by:  imadomg 4816

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-gen 965  ax-ext 1462

This theorem depends on definitions:  df-bi 147  df-an 225  df-cleq 1472  df-fn 3199  df-fo 3202

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