Theorem fnfrn 3634

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 2080	. . 3 |- ran F (_ ran F
2	1	biantru 724	. 2 |- (F Fn A <-> (F Fn A /\ ran F (_ ran F))
3		df-f 3194	. 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 2047  ran crn 3171   Fn wfn 3177  -->wf 3178

This theorem is referenced by:  fsn2 3836  ac6lem 4754  fodom 4798  cncffvrn 7273  bcthlem33 8031  ghomgrpilem2 10386

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 962  ax-gen 963  ax-8 964  ax-10 966  ax-12 968  ax-17 971  ax-4 973  ax-5o 975  ax-6o 978  ax-9o 1123  ax-10o 1140  ax-16 1210  ax-11o 1218  ax-ext 1459

This theorem depends on definitions:  df-bi 147  df-an 225  df-ex 981  df-sb 1172  df-clab 1464  df-cleq 1469  df-clel 1472  df-in 2051  df-ss 2053  df-f 3194

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