Theorem dffn4 5112

Description: A function maps onto its range. (Contributed by NM, 10-May-1998.)

Assertion

Ref	Expression
dffn4	|- ( F Fn A <-> F : A -onto-> ran F )

Proof of Theorem dffn4

Step	Hyp	Ref	Expression
1		eqid 2040	. . 3 |- ran F = ran F
2	1	biantru 286	. 2 |- ( F Fn A <-> ( F Fn A /\ ran F = ran F ) )
3		df-fo 4908	. 2 |- ( F : A -onto-> ran F <-> ( F Fn A /\ ran F = ran F ) )
4	2, 3	bitr4i 176	1 |- ( F Fn A <-> F : A -onto-> ran F )

Syntax hints:   /\ wa 97   <-> wb 98   = wceq 1243   ran crn 4346   Fn wfn 4897   -onto->wfo 4900

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-gen 1338  ax-ext 2022

This theorem depends on definitions:  df-bi 110  df-cleq 2033  df-fo 4908

This theorem is referenced by:  funforn  5113  ffoss  5158  tposf2  5883