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Theorem funmpt2 5291
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
funmpt2.1  |-  F  =  ( x  e.  A  |->  B )
Assertion
Ref Expression
funmpt2  |-  Fun  F

Proof of Theorem funmpt2
StepHypRef Expression
1 funmpt 5290 . 2  |-  Fun  (
x  e.  A  |->  B )
2 funmpt2.1 . . 3  |-  F  =  ( x  e.  A  |->  B )
32funeqi 5275 . 2  |-  ( Fun 
F  <->  Fun  ( x  e.  A  |->  B ) )
41, 3mpbir 200 1  |-  Fun  F
Colors of variables: wff set class
Syntax hints:    = wceq 1623    e. cmpt 4077   Fun wfun 5249
This theorem is referenced by:  tz9.12lem2  7460  tz9.12lem3  7461  rankf  7466  cardf2  7576  fin23lem30  7968  divstgpopn  17802  ballotlem7  23094  sinccvglem  24005  cmpfunOLD  25142  cmpdom  25143  trset  25392  imtr  25398  ltrset  25402  rltrset  25413  trnij  25615  pfsubkl  26047  stoweidlem27  27776  stirlinglem14  27836
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-14 1688  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264  ax-sep 4141  ax-nul 4149  ax-pr 4214
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-eu 2147  df-mo 2148  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-ne 2448  df-ral 2548  df-rex 2549  df-rab 2552  df-v 2790  df-dif 3155  df-un 3157  df-in 3159  df-ss 3166  df-nul 3456  df-if 3566  df-sn 3646  df-pr 3647  df-op 3649  df-br 4024  df-opab 4078  df-mpt 4079  df-id 4309  df-xp 4695  df-rel 4696  df-cnv 4697  df-co 4698  df-fun 5257
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