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Theorem caovclg 5653
 Description: Convert an operation closure law to class notation. (Contributed by Mario Carneiro, 26-May-2014.)
Hypothesis
Ref Expression
caovclg.1
Assertion
Ref Expression
caovclg
Distinct variable groups:   ,,   ,   ,,   ,,   ,,   ,,   ,,
Allowed substitution hint:   ()

Proof of Theorem caovclg
StepHypRef Expression
1 caovclg.1 . . 3
21ralrimivva 2401 . 2
3 oveq1 5519 . . . 4
43eleq1d 2106 . . 3
5 oveq2 5520 . . . 4
65eleq1d 2106 . . 3
74, 6rspc2v 2662 . 2
82, 7mpan9 265 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 97   wceq 1243   wcel 1393  wral 2306  (class class class)co 5512 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-3an 887  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-ral 2311  df-rex 2312  df-v 2559  df-un 2922  df-sn 3381  df-pr 3382  df-op 3384  df-uni 3581  df-br 3765  df-iota 4867  df-fv 4910  df-ov 5515 This theorem is referenced by:  caovcld  5654  caovcl  5655  caovlem2d  5693  grprinvd  5696  frec2uzrdg  9195  frecuzrdgsuc  9201  iseqovex  9219  iseqval  9220  iseqcaopr  9242
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