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Theorem cmpfun 24541
Description: Functionality of a class given by a "maps to" notation. (Contributed by FL, 17-Feb-2008.) (Revised by Mario Carneiro, 31-May-2014.)
Hypothesis
Ref Expression
cmp.1  |-  F  =  ( x  e.  A  |->  B )
Assertion
Ref Expression
cmpfun  |-  Fun  F

Proof of Theorem cmpfun
StepHypRef Expression
1 funmpt 5256 . 2  |-  Fun  (
x  e.  A  |->  B )
2 cmp.1 . . 3  |-  F  =  ( x  e.  A  |->  B )
32funeqi 5241 . 2  |-  ( Fun 
F  <->  Fun  ( x  e.  A  |->  B ) )
41, 3mpbir 202 1  |-  Fun  F
Colors of variables: wff set class
Syntax hints:    = wceq 1624    e. cmpt 4078   Fun wfun 5215
This theorem is referenced by:  cmpdom  24542  trset  24791  imtr  24797  ltrset  24801  rltrset  24812  trnij  25014  pfsubkl  25446
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-gen 1534  ax-5 1545  ax-17 1604  ax-9 1637  ax-8 1645  ax-14 1689  ax-6 1704  ax-7 1709  ax-11 1716  ax-12 1867  ax-ext 2265  ax-sep 4142  ax-nul 4150  ax-pr 4213
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 938  df-tru 1312  df-ex 1530  df-nf 1533  df-sb 1632  df-eu 2148  df-mo 2149  df-clab 2271  df-cleq 2277  df-clel 2280  df-nfc 2409  df-ne 2449  df-ral 2549  df-rex 2550  df-rab 2553  df-v 2791  df-dif 3156  df-un 3158  df-in 3160  df-ss 3167  df-nul 3457  df-if 3567  df-sn 3647  df-pr 3648  df-op 3650  df-br 4025  df-opab 4079  df-mpt 4080  df-id 4308  df-xp 4694  df-rel 4695  df-cnv 4696  df-co 4697  df-fun 5223
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