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Theorem caovassg 6450
 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 2881 . 2
3 oveq1 6284 . . . . 5
43oveq1d 6292 . . . 4
5 oveq1 6284 . . . 4
64, 5eqeq12d 2484 . . 3
7 oveq2 6285 . . . . 5
87oveq1d 6292 . . . 4
9 oveq1 6284 . . . . 5
109oveq2d 6293 . . . 4
118, 10eqeq12d 2484 . . 3
12 oveq2 6285 . . . 4
13 oveq2 6285 . . . . 5
1413oveq2d 6293 . . . 4
1512, 14eqeq12d 2484 . . 3
166, 11, 15rspc3v 3221 . 2
172, 16mpan9 469 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wa 369   w3a 968   wceq 1374   wcel 1762  wral 2809  (class class class)co 6277 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1596  ax-4 1607  ax-5 1675  ax-6 1714  ax-7 1734  ax-10 1781  ax-11 1786  ax-12 1798  ax-13 1963  ax-ext 2440 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 970  df-tru 1377  df-ex 1592  df-nf 1595  df-sb 1707  df-clab 2448  df-cleq 2454  df-clel 2457  df-nfc 2612  df-ral 2814  df-rex 2815  df-rab 2818  df-v 3110  df-dif 3474  df-un 3476  df-in 3478  df-ss 3485  df-nul 3781  df-if 3935  df-sn 4023  df-pr 4025  df-op 4029  df-uni 4241  df-br 4443  df-iota 5544  df-fv 5589  df-ov 6280 This theorem is referenced by:  caovassd  6451  caovass  6452  grprinvlem  6490  grprinvd  6491  grpridd  6492  seqsplit  12098  seqcaopr  12102  seqf1olem2  12105
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