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Theorem anorabs 225
Description: Absorption law for ortholattices. (Contributed by NM, 8-Nov-1998.)
Assertion
Ref Expression
anorabs (a ∩ (b ∪ (a ∩ (ab)))) = (a ∩ (ab))

Proof of Theorem anorabs
StepHypRef Expression
1 anorabs2 224 . 2 (a ∩ (b ∪ (a ∩ (ba)))) = (a ∩ (ba))
2 ax-a2 31 . . . . 5 (ab) = (ba)
32lan 77 . . . 4 (a ∩ (ab)) = (a ∩ (ba))
43lor 70 . . 3 (b ∪ (a ∩ (ab))) = (b ∪ (a ∩ (ba)))
54lan 77 . 2 (a ∩ (b ∪ (a ∩ (ab)))) = (a ∩ (b ∪ (a ∩ (ba))))
61, 5, 33tr1 63 1 (a ∩ (b ∪ (a ∩ (ab)))) = (a ∩ (ab))
Colors of variables: term
Syntax hints:   = wb 1   wn 4  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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