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Theorem fngid 20881
Description: GId is a function. (Contributed by FL, 5-Feb-2010.) (Revised by Mario Carneiro, 15-Dec-2013.) (New usage is discouraged.)
Assertion
Ref Expression
fngid  |- GId  Fn  _V

Proof of Theorem fngid
Dummy variables  u  g  x are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 riotaex 6308 . 2  |-  ( iota_ u  e.  ran  g A. x  e.  ran  g ( ( u g x )  =  x  /\  ( x g u )  =  x ) )  e.  _V
2 df-gid 20859 . 2  |- GId  =  ( g  e.  _V  |->  (
iota_ u  e.  ran  g A. x  e.  ran  g ( ( u g x )  =  x  /\  ( x g u )  =  x ) ) )
31, 2fnmpti 5372 1  |- GId  Fn  _V
Colors of variables: wff set class
Syntax hints:    /\ wa 358    = wceq 1623   A.wral 2543   _Vcvv 2788   ran crn 4690    Fn wfn 5250  (class class class)co 5858   iota_crio 6297  GIdcgi 20854
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-14 1688  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264  ax-sep 4141  ax-nul 4149  ax-pr 4214
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-eu 2147  df-mo 2148  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-ne 2448  df-ral 2548  df-rex 2549  df-rab 2552  df-v 2790  df-sbc 2992  df-dif 3155  df-un 3157  df-in 3159  df-ss 3166  df-nul 3456  df-if 3566  df-sn 3646  df-pr 3647  df-op 3649  df-uni 3828  df-br 4024  df-opab 4078  df-mpt 4079  df-id 4309  df-xp 4695  df-rel 4696  df-cnv 4697  df-co 4698  df-dm 4699  df-iota 5219  df-fun 5257  df-fn 5258  df-fv 5263  df-riota 6304  df-gid 20859
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