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Theorem funmpt2 6587
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 6586 . 2 Fun (𝑥𝐴𝐵)
2 funmpt2.1 . . 3 𝐹 = (𝑥𝐴𝐵)
32funeqi 6569 . 2 (Fun 𝐹 ↔ Fun (𝑥𝐴𝐵))
41, 3mpbir 230 1 Fun 𝐹
Colors of variables: wff setvar class
Syntax hints:   = wceq 1541  cmpt 5231  Fun wfun 6537
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 1913  ax-6 1971  ax-7 2011  ax-8 2108  ax-9 2116  ax-10 2137  ax-11 2154  ax-12 2171  ax-ext 2703  ax-sep 5299  ax-nul 5306  ax-pr 5427
This theorem depends on definitions:  df-bi 206  df-an 397  df-or 846  df-3an 1089  df-tru 1544  df-fal 1554  df-ex 1782  df-nf 1786  df-sb 2068  df-mo 2534  df-eu 2563  df-clab 2710  df-cleq 2724  df-clel 2810  df-nfc 2885  df-ral 3062  df-rex 3071  df-rab 3433  df-v 3476  df-dif 3951  df-un 3953  df-in 3955  df-ss 3965  df-nul 4323  df-if 4529  df-sn 4629  df-pr 4631  df-op 4635  df-br 5149  df-opab 5211  df-mpt 5232  df-id 5574  df-xp 5682  df-rel 5683  df-cnv 5684  df-co 5685  df-fun 6545
This theorem is referenced by:  pwfilem  9176  cantnfp1lem1  9672  tz9.12lem2  9782  tz9.12lem3  9783  rankf  9788  djuun  9920  cardf2  9937  fin23lem30  10336  hashf1rn  14311  oppccatf  17673  funtopon  22421  qustgpopn  23623  ustn0  23724  cphsscph  24767  ipasslem8  30085  xppreima2  31871  funcnvmpt  31887  mptiffisupp  31910  fsuppcurry1  31945  fsuppcurry2  31946  gsummpt2co  32195  zarclsint  32847  zartopn  32850  zarmxt1  32855  zarcmplem  32856  brsiga  33176  sseqval  33382  ballotlem7  33529  sinccvglem  34652  bj-evalfun  35949  bj-ccinftydisj  36089  bj-elccinfty  36090  bj-minftyccb  36101  iscard4  42274  harval3  42279  comptiunov2i  42447  icccncfext  44593  stoweidlem27  44733  stirlinglem14  44793  fourierdlem70  44882  fourierdlem71  44883  hoi2toco  45313  mptcfsupp  47046  lcoc0  47093  lincresunit2  47149
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