Theorem caovdid 6490

Description: Convert an operation distributive law to class notation. (Contributed by Mario Carneiro, 30-Dec-2014.)

Hypotheses

Ref	Expression
caovdig.1
caovdid.2
caovdid.3
caovdid.4

Assertion

Ref	Expression
caovdid

Distinct variable groups:   ,,,   ,,,   ,,,   ,,,   ,,,   ,,,   ,,,   ,,,   ,S,,

Proof of Theorem caovdid

Step	Hyp	Ref	Expression
1		id 22	. 2
2		caovdid.2	. 2
3		caovdid.3	. 2
4		caovdid.4	. 2
5		caovdig.1	. . 3
6	5	caovdig 6489	. 2
7	1, 2, 3, 4, 6	syl13anc 1230	1

Syntax hints:  ->wi 4  /\wa 369  /\w3a 973  =wceq 1395  e.wcel 1818  (class class class)co 6296

This theorem is referenced by:  caovdir2d  6491  caofdi  6576

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