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Theorem funmpt2 5841
 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 5840 . 2 Fun (𝑥𝐴𝐵)
2 funmpt2.1 . . 3 𝐹 = (𝑥𝐴𝐵)
32funeqi 5824 . 2 (Fun 𝐹 ↔ Fun (𝑥𝐴𝐵))
41, 3mpbir 220 1 Fun 𝐹
 Colors of variables: wff setvar class Syntax hints:   = wceq 1475   ↦ cmpt 4643  Fun wfun 5798 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-9 1986  ax-10 2006  ax-11 2021  ax-12 2034  ax-13 2234  ax-ext 2590  ax-sep 4709  ax-nul 4717  ax-pr 4833 This theorem depends on definitions:  df-bi 196  df-or 384  df-an 385  df-3an 1033  df-tru 1478  df-ex 1696  df-nf 1701  df-sb 1868  df-eu 2462  df-mo 2463  df-clab 2597  df-cleq 2603  df-clel 2606  df-nfc 2740  df-ral 2901  df-rab 2905  df-v 3175  df-dif 3543  df-un 3545  df-in 3547  df-ss 3554  df-nul 3875  df-if 4037  df-sn 4126  df-pr 4128  df-op 4132  df-br 4584  df-opab 4644  df-mpt 4645  df-id 4953  df-xp 5044  df-rel 5045  df-cnv 5046  df-co 5047  df-fun 5806 This theorem is referenced by:  cantnfp1lem1  8458  tz9.12lem2  8534  tz9.12lem3  8535  rankf  8540  cardf2  8652  fin23lem30  9047  hashf1rn  13004  hashf1rnOLD  13005  qustgpopn  21733  ustn0  21834  metuval  22164  ipasslem8  27076  xppreima2  28830  funcnvmpt  28851  gsummpt2co  29111  metidval  29261  pstmval  29266  brsiga  29573  measbasedom  29592  sseqval  29777  ballotlem7  29924  sinccvglem  30820  bj-funtopon  32236  bj-ccinftydisj  32277  bj-elccinfty  32278  bj-minftyccb  32289  comptiunov2i  37017  icccncfext  38773  stoweidlem27  38920  stirlinglem14  38980  fourierdlem70  39069  fourierdlem71  39070  hoi2toco  39497  mptcfsupp  41955  lcoc0  42005  lincresunit2  42061
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