Theorem fnforn 2791

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		cleqid 1102	. . 3 |- ran F = ran F
2	1	biantru 543	. 2 |- (F Fn A <-> (F Fn A /\ ran F = ran F))
3		df-fo 2436	. 2 |- (F:A-onto->ran F <-> (F Fn A /\ ran F = ran F))
4	2, 3	bitr4 154	1 |- (F Fn A <-> F:A-onto->ran F)

Syntax hints:   <-> wb 127   /\ wa 196   = wceq 1091  ran crn 2411   Fn wfn 2417  -onto->wfo 2420

This theorem is referenced by:  funforn 2792  ffoss 2820  mapsn 3269  fnrndomg 3617

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6  ax-gen 677  ax-ext 1074

This theorem depends on definitions:  df-bi 128  df-an 198  df-cleq 1097  df-fo 2436

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