Theorem mh2 866

Description: Marsden-Herman distributive law. Corollary 3.3 of Beran, p. 259.

Hypotheses

Ref	Expression
marsden.1	a C b
marsden.2	b C c
marsden.3	c C d
marsden.4	d C a

Assertion

Ref	Expression
mh2	((a v b) ^ (c v d)) = (((a ^ c) v (a ^ d)) v ((b ^ c) v (b ^ d)))

Proof of Theorem mh2

Step	Hyp	Ref	Expression
1		marsden.1	. 2 a C b
2		marsden.4	. . 3 d C a
3	2	comcom 435	. 2 a C d
4		marsden.2	. . 3 b C c
5	4	comcom 435	. 2 c C b
6		marsden.3	. 2 c C d
7	1, 3, 5, 6	mh 861	1 ((a v b) ^ (c v d)) = (((a ^ c) v (a ^ d)) v ((b ^ c) v (b ^ d)))

Syntax hints:   = wb 1   C wc 3   v wo 6   ^ wa 7

This theorem is referenced by:  mhcor1 870

This theorem was proved from axioms:  ax-a1 29  ax-a2 30  ax-a3 31  ax-a4 32  ax-a5 33  ax-r1 34  ax-r2 35  ax-r4 36  ax-r5 37  ax-r3 421

This theorem depends on definitions:  df-b 38  df-a 39  df-t 40  df-f 41  df-le1 122  df-le2 123  df-c1 124  df-c2 125

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