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Theorem wwoml2 212
 Description: Weak orthomodular law. (Contributed by NM, 2-Sep-1997.)
Hypothesis
Ref Expression
wwoml2.1 ab
Assertion
Ref Expression
wwoml2 ((a ∪ (ab)) ≡ b) = 1

Proof of Theorem wwoml2
StepHypRef Expression
1 wwoml2.1 . . . . . . 7 ab
21df-le2 131 . . . . . 6 (ab) = b
32ax-r1 35 . . . . 5 b = (ab)
43lan 77 . . . 4 (ab) = (a ∩ (ab))
54lor 70 . . 3 (a ∪ (ab)) = (a ∪ (a ∩ (ab)))
65rbi 98 . 2 ((a ∪ (ab)) ≡ (ab)) = ((a ∪ (a ∩ (ab))) ≡ (ab))
72lbi 97 . 2 ((a ∪ (ab)) ≡ (ab)) = ((a ∪ (ab)) ≡ b)
8 woml 211 . 2 ((a ∪ (a ∩ (ab))) ≡ (ab)) = 1
96, 7, 83tr2 64 1 ((a ∪ (ab)) ≡ b) = 1
 Colors of variables: term Syntax hints:   = wb 1   ≤ wle 2  ⊥ wn 4   ≡ tb 5   ∪ 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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