Theorem womaa 214

Description: Weak OM-like absorption law for ortholattices.

Assertion

Ref	Expression
womaa	(a_|_ v (a ^ (a_|_ v (a ^ b)))) = (a_|_ v (a ^ b))

Proof of Theorem womaa

Step	Hyp	Ref	Expression
1		leo 150	. . 3 a_|_ =< (a_|_ v (a ^ b))
2		lear 153	. . 3 (a ^ (a_|_ v (a ^ b))) =< (a_|_ v (a ^ b))
3	1, 2	lel2or 162	. 2 (a_|_ v (a ^ (a_|_ v (a ^ b)))) =< (a_|_ v (a ^ b))
4		leo 150	. . 3 a_|_ =< (a_|_ v (a ^ (a_|_ v (a ^ b))))
5		lea 152	. . . . 5 (a ^ b) =< a
6		leor 151	. . . . 5 (a ^ b) =< (a_|_ v (a ^ b))
7	5, 6	ler2an 165	. . . 4 (a ^ b) =< (a ^ (a_|_ v (a ^ b)))
8		leor 151	. . . 4 (a ^ (a_|_ v (a ^ b))) =< (a_|_ v (a ^ (a_|_ v (a ^ b))))
9	7, 8	letr 129	. . 3 (a ^ b) =< (a_|_ v (a ^ (a_|_ v (a ^ b))))
10	4, 9	lel2or 162	. 2 (a_|_ v (a ^ b)) =< (a_|_ v (a ^ (a_|_ v (a ^ b))))
11	3, 10	lebi 137	1 (a_|_ v (a ^ (a_|_ v (a ^ b)))) = (a_|_ v (a ^ b))

Syntax hints:   = wb 1  _|_wn 4   v wo 6   ^ wa 7

This theorem is referenced by:  nom13 302

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

This theorem depends on definitions:  df-a 39  df-t 40  df-f 41  df-le1 122  df-le2 123

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