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Theorem caovcom 6472
 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 455 . 2
4 caovcom.3 . . . 4
54a1i 11 . . 3
65caovcomg 6470 . 2
71, 3, 6mp2an 672 1
 Colors of variables: wff setvar class Syntax hints:  /\wa 369  =wceq 1395  e.wcel 1818   cvv 3109  (class class class)co 6296 This theorem is referenced by:  caovord2  6487  caov32  6502  caov12  6503  caov42  6508  caovdir  6509  caovmo  6512  ecopovsym  7432  ecopover  7434  genpcl  9407 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ral 2812  df-rex 2813  df-rab 2816  df-v 3111  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-nul 3785  df-if 3942  df-sn 4030  df-pr 4032  df-op 4036  df-uni 4250  df-br 4453  df-iota 5556  df-fv 5601  df-ov 6299
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