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Theorem funmpt2 5562
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  =  ( x  e.  A  |->  B )
Assertion
Ref Expression
funmpt2  |-  Fun  F

Proof of Theorem funmpt2
StepHypRef Expression
1 funmpt 5561 . 2  |-  Fun  (
x  e.  A  |->  B )
2 funmpt2.1 . . 3  |-  F  =  ( x  e.  A  |->  B )
32funeqi 5545 . 2  |-  ( Fun 
F  <->  Fun  ( x  e.  A  |->  B ) )
41, 3mpbir 209 1  |-  Fun  F
Colors of variables: wff setvar class
Syntax hints:    = wceq 1405    |-> cmpt 4452   Fun wfun 5519
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1639  ax-4 1652  ax-5 1725  ax-6 1771  ax-7 1814  ax-9 1846  ax-10 1861  ax-11 1866  ax-12 1878  ax-13 2026  ax-ext 2380  ax-sep 4516  ax-nul 4524  ax-pr 4629
This theorem depends on definitions:  df-bi 185  df-or 368  df-an 369  df-3an 976  df-tru 1408  df-ex 1634  df-nf 1638  df-sb 1764  df-eu 2242  df-mo 2243  df-clab 2388  df-cleq 2394  df-clel 2397  df-nfc 2552  df-ne 2600  df-ral 2758  df-rex 2759  df-rab 2762  df-v 3060  df-dif 3416  df-un 3418  df-in 3420  df-ss 3427  df-nul 3738  df-if 3885  df-sn 3972  df-pr 3974  df-op 3978  df-br 4395  df-opab 4453  df-mpt 4454  df-id 4737  df-xp 4948  df-rel 4949  df-cnv 4950  df-co 4951  df-fun 5527
This theorem is referenced by:  cantnfp1lem1  8049  tz9.12lem2  8158  tz9.12lem3  8159  rankf  8164  cardf2  8276  fin23lem30  8674  hashf1rn  12379  qustgpopn  20802  ustn0  20907  metuvalOLD  21236  metuval  21237  ipasslem8  26046  xppreima2  27811  funcnvmpt  27833  gsummpt2co  28102  metidval  28202  pstmval  28207  brsiga  28511  measbasedom  28530  sseqval  28713  ballotlem7  28860  sinccvglem  29771  bj-ccinftydisj  31168  bj-elccinfty  31169  bj-minftyccb  31180  comptiunov2i  35666  icccncfext  37040  stoweidlem27  37159  stirlinglem14  37219  fourierdlem70  37309  fourierdlem71  37310  mptcfsupp  38464  lcoc0  38514  lincresunit2  38570
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