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Theorem caovdig 6489
 Description: Convert an operation distributive law to class notation. (Contributed by NM, 25-Aug-1995.) (Revised by Mario Carneiro, 26-Jul-2014.)
Hypothesis
Ref Expression
caovdig.1
Assertion
Ref Expression
caovdig
Distinct variable groups:   ,,,   ,,,   ,,,   ,,,   ,,,   ,,,   ,,,   ,,,   ,S,,

Proof of Theorem caovdig
StepHypRef Expression
1 caovdig.1 . . 3
21ralrimivvva 2879 . 2
3 oveq1 6303 . . . 4
4 oveq1 6303 . . . . 5
5 oveq1 6303 . . . . 5
64, 5oveq12d 6314 . . . 4
73, 6eqeq12d 2479 . . 3
8 oveq1 6303 . . . . 5
98oveq2d 6312 . . . 4
10 oveq2 6304 . . . . 5
1110oveq1d 6311 . . . 4
129, 11eqeq12d 2479 . . 3
13 oveq2 6304 . . . . 5
1413oveq2d 6312 . . . 4
15 oveq2 6304 . . . . 5
1615oveq2d 6312 . . . 4
1714, 16eqeq12d 2479 . . 3
187, 12, 17rspc3v 3222 . 2
192, 18mpan9 469 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4  /\wa 369  /\w3a 973  =wceq 1395  e.wcel 1818  A.wral 2807  (class class class)co 6296 This theorem is referenced by:  caovdid  6490  caovdi  6494  srgi  17163  ringi  17211 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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