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Theorem omlan 448
Description: Orthomodular law.
Assertion
Ref Expression
omlan (a' ^ (a v (a' ^ b))) = (a' ^ b)
Proof of Theorem omlan
StepHypRef Expression
1 ax-a1 30 . . . 4 a = a''
21ax-r5 38 . . 3 (a v (a' ^ b)) = (a'' v (a' ^ b))
32lan 77 . 2 (a' ^ (a v (a' ^ b))) = (a' ^ (a'' v (a' ^ b)))
4 omla 447 . 2 (a' ^ (a'' v (a' ^ b))) = (a' ^ b)
53, 4ax-r2 36 1 (a' ^ (a v (a' ^ b))) = (a' ^ 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:  i3lem1  504  i3lem3  506  u1lem8  776  u3lem10  785  3vth1  804  1oaii  824  mlaconjolem  885  oatr  928  oalii  1002  oaliv  1003
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