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Theorem caovassg 5659
 Description: Convert an operation associative law to class notation. (Contributed by Mario Carneiro, 1-Jun-2013.) (Revised by Mario Carneiro, 26-May-2014.)
Hypothesis
Ref Expression
caovassg.1
Assertion
Ref Expression
caovassg
Distinct variable groups:   ,,,   ,,,   ,,,   ,,,   ,,,   ,,,

Proof of Theorem caovassg
StepHypRef Expression
1 caovassg.1 . . 3
21ralrimivvva 2402 . 2
3 oveq1 5519 . . . . 5
43oveq1d 5527 . . . 4
5 oveq1 5519 . . . 4
64, 5eqeq12d 2054 . . 3
7 oveq2 5520 . . . . 5
87oveq1d 5527 . . . 4
9 oveq1 5519 . . . . 5
109oveq2d 5528 . . . 4
118, 10eqeq12d 2054 . . 3
12 oveq2 5520 . . . 4
13 oveq2 5520 . . . . 5
1413oveq2d 5528 . . . 4
1512, 14eqeq12d 2054 . . 3
166, 11, 15rspc3v 2665 . 2
172, 16mpan9 265 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 97   w3a 885   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:  caovassd  5660  caovass  5661  grprinvlem  5695  grprinvd  5696  grpridd  5697  iseqsplit  9238  iseqcaopr  9242
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