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Theorem fngid 20897
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 6324 . 2  |-  ( iota_ u  e.  ran  g A. x  e.  ran  g ( ( u g x )  =  x  /\  ( x g u )  =  x ) )  e.  _V
2 df-gid 20875 . 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 5388 1  |- GId  Fn  _V
Colors of variables: wff set class
Syntax hints:    /\ wa 358    = wceq 1632   A.wral 2556   _Vcvv 2801   ran crn 4706    Fn wfn 5266  (class class class)co 5874   iota_crio 6313  GIdcgi 20870
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-14 1700  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277  ax-sep 4157  ax-nul 4165  ax-pr 4230
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-eu 2160  df-mo 2161  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-ne 2461  df-ral 2561  df-rex 2562  df-rab 2565  df-v 2803  df-sbc 3005  df-dif 3168  df-un 3170  df-in 3172  df-ss 3179  df-nul 3469  df-if 3579  df-sn 3659  df-pr 3660  df-op 3662  df-uni 3844  df-br 4040  df-opab 4094  df-mpt 4095  df-id 4325  df-xp 4711  df-rel 4712  df-cnv 4713  df-co 4714  df-dm 4715  df-iota 5235  df-fun 5273  df-fn 5274  df-fv 5279  df-riota 6320  df-gid 20875
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