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Theorem oml2 451
Description: Orthomodular law. Kalmbach 83 p. 22. (Contributed by NM, 27-Aug-1997.)
Hypothesis
Ref Expression
oml2.1 ab
Assertion
Ref Expression
oml2 (a ∪ (ab)) = b

Proof of Theorem oml2
StepHypRef Expression
1 oml 445 . 2 (a ∪ (a ∩ (ab))) = (ab)
2 oml2.1 . . . . 5 ab
32df-le2 131 . . . 4 (ab) = b
43lan 77 . . 3 (a ∩ (ab)) = (ab)
54lor 70 . 2 (a ∪ (a ∩ (ab))) = (a ∪ (ab))
61, 5, 33tr2 64 1 (a ∪ (ab)) = b
Colors of variables: term
Syntax hints:   = wb 1  wle 2   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  ax-r3 439
This theorem depends on definitions:  df-b 39  df-a 40  df-t 41  df-f 42  df-le2 131
This theorem is referenced by:  oml3  452  comcom  453  com3i  467  lem4  511  lem4.6.6i4j2  1101
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