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Theorem caovdirg 6267
 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 2801 . 2
3 oveq1 6091 . . . . 5
43oveq1d 6099 . . . 4
5 oveq1 6091 . . . . 5
65oveq1d 6099 . . . 4
74, 6eqeq12d 2452 . . 3
8 oveq2 6092 . . . . 5
98oveq1d 6099 . . . 4
10 oveq1 6091 . . . . 5
1110oveq2d 6100 . . . 4
129, 11eqeq12d 2452 . . 3
13 oveq2 6092 . . . 4
14 oveq2 6092 . . . . 5
15 oveq2 6092 . . . . 5
1614, 15oveq12d 6102 . . . 4
1713, 16eqeq12d 2452 . . 3
187, 12, 17rspc3v 3063 . 2
192, 18mpan9 457 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 360   w3a 937   wceq 1653   wcel 1726  wral 2707  (class class class)co 6084 This theorem is referenced by:  caovdird  6268  rngi  15681 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ral 2712  df-rex 2713  df-rab 2716  df-v 2960  df-dif 3325  df-un 3327  df-in 3329  df-ss 3336  df-nul 3631  df-if 3742  df-sn 3822  df-pr 3823  df-op 3825  df-uni 4018  df-br 4216  df-iota 5421  df-fv 5465  df-ov 6087
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