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Theorem anorabs 225
Description: Absorption law for ortholattices.
Assertion
Ref Expression
anorabs (a' ^ (b v (a' ^ (a v b)))) = (a' ^ (a v b))
Proof of Theorem anorabs
StepHypRef Expression
1 anorabs2 224 . 2 (a' ^ (b v (a' ^ (b v a)))) = (a' ^ (b v a))
2 ax-a2 31 . . . . 5 (a v b) = (b v a)
32lan 77 . . . 4 (a' ^ (a v b)) = (a' ^ (b v a))
43lor 70 . . 3 (b v (a' ^ (a v b))) = (b v (a' ^ (b v a)))
54lan 77 . 2 (a' ^ (b v (a' ^ (a v b)))) = (a' ^ (b v (a' ^ (b v a))))
61, 5, 33tr1 63 1 (a' ^ (b v (a' ^ (a v b)))) = (a' ^ (a v b))
Colors of variables: term
Syntax hints:   = wb 1  'wn 4   v wo 6   ^ wa 7
This theorem was proved from axioms:  ax-a1 30  ax-a2 31  ax-a3 32  ax-a5 34  ax-r1 35  ax-r2 36  ax-r4 37  ax-r5 38
This theorem depends on definitions:  df-a 40  df-t 41  df-f 42  df-le1 130  df-le2 131
This theorem is referenced by: (None)
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