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Theorem cmpfun 24495
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 5215 . 2  |-  Fun  (
x  e.  A  |->  B )
2 cmp.1 . . 3  |-  F  =  ( x  e.  A  |->  B )
32funeqi 5200 . 2  |-  ( Fun 
F  <->  Fun  ( x  e.  A  |->  B ) )
41, 3mpbir 202 1  |-  Fun  F
Colors of variables: wff set class
Syntax hints:    = wceq 1619    e. cmpt 4037   Fun wfun 4653
This theorem is referenced by:  cmpdom  24496  trset  24745  imtr  24751  ltrset  24755  rltrset  24766  trnij  24968  pfsubkl  25400
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-6 1534  ax-7 1535  ax-gen 1536  ax-8 1623  ax-11 1624  ax-14 1626  ax-17 1628  ax-12o 1664  ax-10 1678  ax-9 1684  ax-4 1692  ax-16 1927  ax-ext 2237  ax-sep 4101  ax-nul 4109  ax-pr 4172
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 941  df-tru 1315  df-ex 1538  df-nf 1540  df-sb 1884  df-eu 2121  df-mo 2122  df-clab 2243  df-cleq 2249  df-clel 2252  df-nfc 2381  df-ne 2421  df-ral 2521  df-rex 2522  df-rab 2525  df-v 2759  df-dif 3116  df-un 3118  df-in 3120  df-ss 3127  df-nul 3417  df-if 3526  df-sn 3606  df-pr 3607  df-op 3609  df-br 3984  df-opab 4038  df-mpt 4039  df-id 4267  df-xp 4661  df-rel 4662  df-cnv 4663  df-co 4664  df-fun 4669
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