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Theorem caovcomg 6242
 Description: Convert an operation commutative law to class notation. (Contributed by Mario Carneiro, 1-Jun-2013.)
Hypothesis
Ref Expression
caovcomg.1
Assertion
Ref Expression
caovcomg
Distinct variable groups:   ,,   ,,   ,,   ,,   ,,

Proof of Theorem caovcomg
StepHypRef Expression
1 caovcomg.1 . . 3
21ralrimivva 2798 . 2
3 oveq1 6088 . . . 4
4 oveq2 6089 . . . 4
53, 4eqeq12d 2450 . . 3
6 oveq2 6089 . . . 4
7 oveq1 6088 . . . 4
86, 7eqeq12d 2450 . . 3
95, 8rspc2v 3058 . 2
102, 9mpan9 456 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 359   wceq 1652   wcel 1725  wral 2705  (class class class)co 6081 This theorem is referenced by:  caovcomd  6243  caovcom  6244  caofcom  6336  seqcaopr  11360  cmncom  15428 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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