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Theorem caovdirg 6477
 Description: Convert an operation reverse distributive law to class notation. (Contributed by Mario Carneiro, 19-Oct-2014.)
Hypothesis
Ref Expression
caovdirg.1
Assertion
Ref Expression
caovdirg
Distinct variable groups:   ,,,   ,,,   ,,,   ,,,   ,,,   ,,,   ,,,   ,,,   ,,,

Proof of Theorem caovdirg
StepHypRef Expression
1 caovdirg.1 . . 3
21ralrimivvva 2865 . 2
3 oveq1 6288 . . . . 5
43oveq1d 6296 . . . 4
5 oveq1 6288 . . . . 5
65oveq1d 6296 . . . 4
74, 6eqeq12d 2465 . . 3
8 oveq2 6289 . . . . 5
98oveq1d 6296 . . . 4
10 oveq1 6288 . . . . 5
1110oveq2d 6297 . . . 4
129, 11eqeq12d 2465 . . 3
13 oveq2 6289 . . . 4
14 oveq2 6289 . . . . 5
15 oveq2 6289 . . . . 5
1614, 15oveq12d 6299 . . . 4
1713, 16eqeq12d 2465 . . 3
187, 12, 17rspc3v 3208 . 2
192, 18mpan9 469 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wa 369   w3a 974   wceq 1383   wcel 1804  wral 2793  (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:  caovdird  6478  srgi  17037  ringi  17085
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