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Theorem wwoml2 212
Description: Weak orthomodular law.
Hypothesis
Ref Expression
wwoml2.1 a =< b
Assertion
Ref Expression
wwoml2 ((a v (a' ^ b)) == b) = 1
Proof of Theorem wwoml2
StepHypRef Expression
1 wwoml2.1 . . . . . . 7 a =< b
21df-le2 131 . . . . . 6 (a v b) = b
32ax-r1 35 . . . . 5 b = (a v b)
43lan 77 . . . 4 (a' ^ b) = (a' ^ (a v b))
54lor 70 . . 3 (a v (a' ^ b)) = (a v (a' ^ (a v b)))
65rbi 98 . 2 ((a v (a' ^ b)) == (a v b)) = ((a v (a' ^ (a v b))) == (a v b))
72lbi 97 . 2 ((a v (a' ^ b)) == (a v b)) = ((a v (a' ^ b)) == b)
8 woml 211 . 2 ((a v (a' ^ (a v b))) == (a v b)) = 1
96, 7, 83tr2 64 1 ((a v (a' ^ b)) == b) = 1
Colors of variables: term
Syntax hints:   = wb 1   =< wle 2  'wn 4   == tb 5   v wo 6   ^ wa 7  1wt 8
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-b 39  df-a 40  df-t 41  df-f 42  df-le2 131
This theorem is referenced by:  wwoml3  213
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