Theorem dffn2 4563

Description: Any function is a mapping into _V. (The proof was shortened by Andrew Salmon, 17-Sep-2011.)

Assertion

Ref	Expression
dffn2	|- (F Fn A <-> F:A-->_V)

Proof of Theorem dffn2

Step	Hyp	Ref	Expression
1		ssv 2636	. . 3 |- ran F C_ _V
2	1	biantru 793	. 2 |- (F Fn A <-> (F Fn A /\ ran F C_ _V))
3		df-f 4010	. 2 |- (F:A-->_V <-> (F Fn A /\ ran F C_ _V))
4	2, 3	bitr4i 193	1 |- (F Fn A <-> F:A-->_V)

Syntax hints:   <-> wb 163   /\ wa 240  _Vcvv 2292   C_ wss 2593  ran crn 3987   Fn wfn 3993  -->wf 3994

This theorem is referenced by:  f1cnv 4611  fnressn 4812  1stcof 5040  fnoprab2g 5063  tz7.48lem 5164  uzrdgfnuzi 7718

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 1304  ax-gen 1305  ax-8 1306  ax-10 1308  ax-12 1310  ax-17 1317  ax-4 1319  ax-5o 1321  ax-6o 1324  ax-9o 1481  ax-10o 1500  ax-16 1580  ax-11o 1588  ax-ext 1865

This theorem depends on definitions:  df-bi 164  df-an 242  df-ex 1327  df-sb 1536  df-clab 1872  df-cleq 1877  df-clel 1880  df-v 2294  df-in 2603  df-ss 2605  df-f 4010

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