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Theorem caovassg 6245
 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 2799 . 2
3 oveq1 6088 . . . . 5
43oveq1d 6096 . . . 4
5 oveq1 6088 . . . 4
64, 5eqeq12d 2450 . . 3
7 oveq2 6089 . . . . 5
87oveq1d 6096 . . . 4
9 oveq1 6088 . . . . 5
109oveq2d 6097 . . . 4
118, 10eqeq12d 2450 . . 3
12 oveq2 6089 . . . 4
13 oveq2 6089 . . . . 5
1413oveq2d 6097 . . . 4
1512, 14eqeq12d 2450 . . 3
166, 11, 15rspc3v 3061 . 2
172, 16mpan9 456 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 359   w3a 936   wceq 1652   wcel 1725  wral 2705  (class class class)co 6081 This theorem is referenced by:  caovassd  6246  caovass  6247  grprinvlem  6285  grprinvd  6286  grpridd  6287  seqsplit  11356  seqcaopr  11360  seqf1olem2  11363 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-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417 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-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ral 2710  df-rex 2711  df-rab 2714  df-v 2958  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-br 4213  df-iota 5418  df-fv 5462  df-ov 6084
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