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Theorem caovcom 5818
 Description: Convert an operation commutative law to class notation. (Contributed by NM, 26-Aug-1995.) (Revised by Mario Carneiro, 1-Jun-2013.)
Hypotheses
Ref Expression
caovcom.1
caovcom.2
caovcom.3
Assertion
Ref Expression
caovcom
Distinct variable groups:   ,,   ,,   ,,

Proof of Theorem caovcom
StepHypRef Expression
1 caovcom.1 . 2
2 caovcom.2 . . 3
31, 2pm3.2i 267 . 2
4 caovcom.3 . . . 4
54a1i 9 . . 3
65caovcomg 5816 . 2
71, 3, 6mp2an 418 1
 Colors of variables: wff set class Syntax hints:   wa 103   wceq 1290   wcel 1439  cvv 2622  (class class class)co 5668 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 666  ax-5 1382  ax-7 1383  ax-gen 1384  ax-ie1 1428  ax-ie2 1429  ax-8 1441  ax-10 1442  ax-11 1443  ax-i12 1444  ax-bndl 1445  ax-4 1446  ax-17 1465  ax-i9 1469  ax-ial 1473  ax-i5r 1474  ax-ext 2071 This theorem depends on definitions:  df-bi 116  df-3an 927  df-tru 1293  df-nf 1396  df-sb 1694  df-clab 2076  df-cleq 2082  df-clel 2085  df-nfc 2218  df-ral 2365  df-rex 2366  df-v 2624  df-un 3006  df-sn 3458  df-pr 3459  df-op 3461  df-uni 3662  df-br 3854  df-iota 4995  df-fv 5038  df-ov 5671 This theorem is referenced by:  caovord2  5833  caov32  5848  caov12  5849  ecopovsym  6404  ecopover  6406
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