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Theorem caovdir2d 6491
 Description: Convert an operation distributive law to class notation. (Contributed by Mario Carneiro, 30-Dec-2014.)
Hypotheses
Ref Expression
caovdir2d.1
caovdir2d.2
caovdir2d.3
caovdir2d.4
caovdir2d.cl
caovdir2d.com
Assertion
Ref Expression
caovdir2d
Distinct variable groups:   ,,,   ,,,   ,,,   ,,,   ,,,   ,,,   ,S,,

Proof of Theorem caovdir2d
StepHypRef Expression
1 caovdir2d.1 . . 3
2 caovdir2d.4 . . 3
3 caovdir2d.2 . . 3
4 caovdir2d.3 . . 3
51, 2, 3, 4caovdid 6490 . 2
6 caovdir2d.com . . 3
7 caovdir2d.cl . . . 4
87, 3, 4caovcld 6468 . . 3
96, 8, 2caovcomd 6471 . 2
106, 3, 2caovcomd 6471 . . 3
116, 4, 2caovcomd 6471 . . 3
1210, 11oveq12d 6314 . 2
135, 9, 123eqtr4d 2508 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4  /\wa 369  /\w3a 973  =wceq 1395  e.wcel 1818  (class class class)co 6296 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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