Users' Mathboxes Mathbox for Frédéric Liné < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  cmpfun Unicode version

Theorem cmpfun 24308
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 5148 . 2  |-  Fun  (
x  e.  A  |->  B )
2 cmp.1 . . 3  |-  F  =  ( x  e.  A  |->  B )
32funeqi 5133 . 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 3974   Fun wfun 4586
This theorem is referenced by:  cmpdom  24309  trset  24558  imtr  24564  ltrset  24568  rltrset  24579  trnij  24781  pfsubkl  25213
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 1926  ax-ext 2234  ax-sep 4038  ax-nul 4046  ax-pr 4108
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 1883  df-eu 2118  df-mo 2119  df-clab 2240  df-cleq 2246  df-clel 2249  df-nfc 2374  df-ne 2414  df-ral 2513  df-rex 2514  df-rab 2516  df-v 2729  df-dif 3081  df-un 3083  df-in 3085  df-ss 3089  df-nul 3363  df-if 3471  df-sn 3550  df-pr 3551  df-op 3553  df-br 3921  df-opab 3975  df-mpt 3976  df-id 4202  df-xp 4594  df-rel 4595  df-cnv 4596  df-co 4597  df-fun 4602
  Copyright terms: Public domain W3C validator