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Theorem cidfn 13904
 Description: The identity arrow operator is a function from objects to arrows. (Contributed by Mario Carneiro, 4-Jan-2017.)
Hypotheses
Ref Expression
cidfn.b
cidfn.i
Assertion
Ref Expression
cidfn

Proof of Theorem cidfn
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 riotaex 6553 . . 3 comp comp
2 eqid 2436 . . 3 comp comp comp comp
31, 2fnmpti 5573 . 2 comp comp
4 cidfn.b . . . 4
5 eqid 2436 . . . 4
6 eqid 2436 . . . 4 comp comp
7 id 20 . . . 4
8 cidfn.i . . . 4
94, 5, 6, 7, 8cidfval 13901 . . 3 comp comp
109fneq1d 5536 . 2 comp comp
113, 10mpbiri 225 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 359   wceq 1652   wcel 1725  wral 2705  cop 3817   cmpt 4266   wfn 5449  cfv 5454  (class class class)co 6081  crio 6542  cbs 13469   chom 13540  compcco 13541  ccat 13889  ccid 13890 This theorem is referenced by:  oppccatid  13945  fucidcl  14162  fucsect  14169  curfcl  14329  curf2ndf  14344 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417  ax-rep 4320  ax-sep 4330  ax-nul 4338  ax-pr 4403 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-eu 2285  df-mo 2286  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ne 2601  df-ral 2710  df-rex 2711  df-reu 2712  df-rab 2714  df-v 2958  df-sbc 3162  df-csb 3252  df-dif 3323  df-un 3325  df-in 3327  df-ss 3334  df-nul 3629  df-if 3740  df-sn 3820  df-pr 3821  df-op 3823  df-uni 4016  df-iun 4095  df-br 4213  df-opab 4267  df-mpt 4268  df-id 4498  df-xp 4884  df-rel 4885  df-cnv 4886  df-co 4887  df-dm 4888  df-rn 4889  df-res 4890  df-ima 4891  df-iota 5418  df-fun 5456  df-fn 5457  df-f 5458  df-f1 5459  df-fo 5460  df-f1o 5461  df-fv 5462  df-ov 6084  df-riota 6549  df-cid 13894
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