Theorem fnfrn 3640

Description: A function maps to its range.

Assertion

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

Proof of Theorem fnfrn

Step	Hyp	Ref	Expression
1		ssid 2083	. . 3 |- ran F (_ ran F
2	1	biantru 726	. 2 |- (F Fn A <-> (F Fn A /\ ran F (_ ran F))
3		df-f 3200	. 2 |- (F:A-->ran F <-> (F Fn A /\ ran F (_ ran F))
4	2, 3	bitr4 176	1 |- (F Fn A <-> F:A-->ran F)

Syntax hints:   <-> wb 146   /\ wa 223   (_ wss 2050  ran crn 3177   Fn wfn 3183  -->wf 3184

This theorem is referenced by:  fsn2 3842  ac6lem 4764  fodom 4808  cncffvrn 7273  bcthlem33 8028  ghomgrpilem2 10381

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 964  ax-gen 965  ax-8 966  ax-10 968  ax-12 970  ax-17 973  ax-4 975  ax-5o 977  ax-6o 980  ax-9o 1125  ax-10o 1142  ax-16 1212  ax-11o 1220  ax-ext 1462

This theorem depends on definitions:  df-bi 147  df-an 225  df-ex 983  df-sb 1174  df-clab 1467  df-cleq 1472  df-clel 1475  df-in 2054  df-ss 2056  df-f 3200

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