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Theorem funmpt2 6382
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 = (𝑥𝐴𝐵)
Assertion
Ref Expression
funmpt2 Fun 𝐹

Proof of Theorem funmpt2
StepHypRef Expression
1 funmpt 6381 . 2 Fun (𝑥𝐴𝐵)
2 funmpt2.1 . . 3 𝐹 = (𝑥𝐴𝐵)
32funeqi 6364 . 2 (Fun 𝐹 ↔ Fun (𝑥𝐴𝐵))
41, 3mpbir 234 1 Fun 𝐹
Colors of variables: wff setvar class
Syntax hints:   = wceq 1538  cmpt 5132  Fun wfun 6337
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912  ax-6 1971  ax-7 2016  ax-8 2117  ax-9 2125  ax-10 2146  ax-11 2162  ax-12 2179  ax-ext 2796  ax-sep 5189  ax-nul 5196  ax-pr 5317
This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-3an 1086  df-tru 1541  df-ex 1782  df-nf 1786  df-sb 2071  df-mo 2624  df-eu 2655  df-clab 2803  df-cleq 2817  df-clel 2896  df-nfc 2964  df-ral 3138  df-v 3482  df-dif 3922  df-un 3924  df-in 3926  df-ss 3936  df-nul 4277  df-if 4451  df-sn 4551  df-pr 4553  df-op 4557  df-br 5053  df-opab 5115  df-mpt 5133  df-id 5447  df-xp 5548  df-rel 5549  df-cnv 5550  df-co 5551  df-fun 6345
This theorem is referenced by:  cantnfp1lem1  9138  tz9.12lem2  9214  tz9.12lem3  9215  rankf  9220  djuun  9352  cardf2  9369  fin23lem30  9762  hashf1rn  13718  funtopon  21528  qustgpopn  22728  ustn0  22829  metuval  23159  cphsscph  23858  ipasslem8  28623  xppreima2  30406  funcnvmpt  30423  fsuppcurry1  30472  fsuppcurry2  30473  gsummpt2co  30718  metidval  31190  pstmval  31195  brsiga  31499  measbasedom  31518  sseqval  31703  ballotlem7  31850  sinccvglem  32972  bj-evalfun  34432  bj-ccinftydisj  34573  bj-elccinfty  34574  bj-minftyccb  34585  iscard4  40157  harval3  40160  comptiunov2i  40323  icccncfext  42455  stoweidlem27  42595  stirlinglem14  42655  fourierdlem70  42744  fourierdlem71  42745  hoi2toco  43172  mptcfsupp  44708  lcoc0  44757  lincresunit2  44813
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