Theorem fnforn 3668

Description: A function maps onto its range.

Assertion

Ref	Expression
fnforn	|- (F Fn A <-> F:A-onto->ran F)

Proof of Theorem fnforn

Step	Hyp	Ref	Expression
1		eqid 1473	. . 3 |- ran F = ran F
2	1	biantru 723	. 2 |- (F Fn A <-> (F Fn A /\ ran F = ran F))
3		df-fo 3191	. 2 |- (F:A-onto->ran F <-> (F Fn A /\ ran F = ran F))
4	2, 3	bitr4 176	1 |- (F Fn A <-> F:A-onto->ran F)

Syntax hints:   <-> wb 146   /\ wa 223   = wceq 954  ran crn 3166   Fn wfn 3172  -onto->wfo 3175

This theorem is referenced by:  funforn 3669  ffoss 3702  mapsn 4335  iunfi 4549  pwfilem 4550  fnrndomg 4787

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-gen 961  ax-ext 1457

This theorem depends on definitions:  df-bi 147  df-an 225  df-cleq 1467  df-fo 3191

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