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Theorem caovordg 6467
 Description: Convert an operation ordering law to class notation. (Contributed by NM, 19-Feb-1996.) (Revised by Mario Carneiro, 30-Dec-2014.)
Hypothesis
Ref Expression
caovordg.1
Assertion
Ref Expression
caovordg
Distinct variable groups:   ,,,   ,,,   ,,,   ,,,   ,,,   ,,,   ,,,

Proof of Theorem caovordg
StepHypRef Expression
1 caovordg.1 . . 3
21ralrimivvva 2865 . 2
3 breq1 4440 . . . 4
4 oveq2 6289 . . . . 5
54breq1d 4447 . . . 4
63, 5bibi12d 321 . . 3
7 breq2 4441 . . . 4
8 oveq2 6289 . . . . 5
98breq2d 4449 . . . 4
107, 9bibi12d 321 . . 3
11 oveq1 6288 . . . . 5
12 oveq1 6288 . . . . 5
1311, 12breq12d 4450 . . . 4
1413bibi2d 318 . . 3
156, 10, 14rspc3v 3208 . 2
162, 15mpan9 469 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 184   wa 369   w3a 974   wceq 1383   wcel 1804  wral 2793   class class class wbr 4437  (class class class)co 6281 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1605  ax-4 1618  ax-5 1691  ax-6 1734  ax-7 1776  ax-10 1823  ax-11 1828  ax-12 1840  ax-13 1985  ax-ext 2421 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 976  df-tru 1386  df-ex 1600  df-nf 1604  df-sb 1727  df-clab 2429  df-cleq 2435  df-clel 2438  df-nfc 2593  df-ral 2798  df-rex 2799  df-rab 2802  df-v 3097  df-dif 3464  df-un 3466  df-in 3468  df-ss 3475  df-nul 3771  df-if 3927  df-sn 4015  df-pr 4017  df-op 4021  df-uni 4235  df-br 4438  df-iota 5541  df-fv 5586  df-ov 6284 This theorem is referenced by:  caovordd  6468
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