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Theorem omln 446
Description: Orthomodular law.
Assertion
Ref Expression
omln (a' v (a ^ (a' v b))) = (a' v b)
Proof of Theorem omln
StepHypRef Expression
1 ax-a1 30 . . . 4 a = a''
21ran 78 . . 3 (a ^ (a' v b)) = (a'' ^ (a' v b))
32lor 70 . 2 (a' v (a ^ (a' v b))) = (a' v (a'' ^ (a' v b)))
4 oml 445 . 2 (a' v (a'' ^ (a' v b))) = (a' v b)
53, 4ax-r2 36 1 (a' v (a ^ (a' v b))) = (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  ax-r3 439
This theorem depends on definitions:  df-b 39  df-a 40  df-t 41  df-f 42
This theorem is referenced by:  omla  447  i3lem4  507  lem4  511  i3abs1  522  u3lemona  627  kb10iii  893  lem4.6.6i3j0  1096  lem4.6.6i3j1  1097
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