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Theorem funmpt2 5623
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 5622 . 2  |-  Fun  (
x  e.  A  |->  B )
2 funmpt2.1 . . 3  |-  F  =  ( x  e.  A  |->  B )
32funeqi 5606 . 2  |-  ( Fun 
F  <->  Fun  ( x  e.  A  |->  B ) )
41, 3mpbir 209 1  |-  Fun  F
Colors of variables: wff setvar class
Syntax hints:    = wceq 1379    |-> cmpt 4505   Fun wfun 5580
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-9 1771  ax-10 1786  ax-11 1791  ax-12 1803  ax-13 1968  ax-ext 2445  ax-sep 4568  ax-nul 4576  ax-pr 4686
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1382  df-ex 1597  df-nf 1600  df-sb 1712  df-eu 2279  df-mo 2280  df-clab 2453  df-cleq 2459  df-clel 2462  df-nfc 2617  df-ne 2664  df-ral 2819  df-rex 2820  df-rab 2823  df-v 3115  df-dif 3479  df-un 3481  df-in 3483  df-ss 3490  df-nul 3786  df-if 3940  df-sn 4028  df-pr 4030  df-op 4034  df-br 4448  df-opab 4506  df-mpt 4507  df-id 4795  df-xp 5005  df-rel 5006  df-cnv 5007  df-co 5008  df-fun 5588
This theorem is referenced by:  cantnfp1lem1  8093  tz9.12lem2  8202  tz9.12lem3  8203  rankf  8208  cardf2  8320  fin23lem30  8718  hashf1rn  12389  divstgpopn  20353  ustn0  20458  metuvalOLD  20787  metuval  20788  ipasslem8  25428  xppreima2  27160  funcnvmpt  27182  gsummpt2co  27434  metidval  27505  pstmval  27510  brsiga  27794  measbasedom  27813  sseqval  27967  ballotlem7  28114  sinccvglem  28513  icccncfext  31226  stoweidlem27  31327  stirlinglem14  31387  fourierdlem70  31477  fourierdlem71  31478  mptcfsupp  32046  lcoc0  32096  lincresunit2  32152  bj-ccinftydisj  33688  bj-elccinfty  33689  bj-minftyccb  33700
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