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Theorem caovdig 5938
 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:   ,,,   ,,,   ,,,   ,,,   ,,,   ,,,   ,,,   ,,,   ,,,

Proof of Theorem caovdig
StepHypRef Expression
1 caovdig.1 . . 3
21ralrimivvva 2513 . 2
3 oveq1 5774 . . . 4
4 oveq1 5774 . . . . 5
5 oveq1 5774 . . . . 5
64, 5oveq12d 5785 . . . 4
73, 6eqeq12d 2152 . . 3
8 oveq1 5774 . . . . 5
98oveq2d 5783 . . . 4
10 oveq2 5775 . . . . 5
1110oveq1d 5782 . . . 4
129, 11eqeq12d 2152 . . 3
13 oveq2 5775 . . . . 5
1413oveq2d 5783 . . . 4
15 oveq2 5775 . . . . 5
1615oveq2d 5783 . . . 4
1714, 16eqeq12d 2152 . . 3
187, 12, 17rspc3v 2800 . 2
192, 18mpan9 279 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 103   w3a 962   wceq 1331   wcel 1480  wral 2414  (class class class)co 5767 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2119 This theorem depends on definitions:  df-bi 116  df-3an 964  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2124  df-cleq 2130  df-clel 2133  df-nfc 2268  df-ral 2419  df-rex 2420  df-v 2683  df-un 3070  df-sn 3528  df-pr 3529  df-op 3531  df-uni 3732  df-br 3925  df-iota 5083  df-fv 5126  df-ov 5770 This theorem is referenced by:  caovdid  5939  caovdi  5943
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