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Theorem wwoml3 213
 Description: Weak orthomodular law. (Contributed by NM, 2-Sep-1997.)
Hypotheses
Ref Expression
wwoml3.1 ab
wwoml3.2 (ba ) = 0
Assertion
Ref Expression
wwoml3 (ab) = 1

Proof of Theorem wwoml3
StepHypRef Expression
1 wwoml3.2 . . . . . 6 (ba ) = 0
21ax-r1 35 . . . . 5 0 = (ba )
3 ancom 74 . . . . 5 (ba ) = (ab)
42, 3ax-r2 36 . . . 4 0 = (ab)
54lor 70 . . 3 (a ∪ 0) = (a ∪ (ab))
65rbi 98 . 2 ((a ∪ 0) ≡ b) = ((a ∪ (ab)) ≡ b)
7 or0 102 . . 3 (a ∪ 0) = a
87rbi 98 . 2 ((a ∪ 0) ≡ b) = (ab)
9 wwoml3.1 . . 3 ab
109wwoml2 212 . 2 ((a ∪ (ab)) ≡ b) = 1
116, 8, 103tr2 64 1 (ab) = 1
 Colors of variables: term Syntax hints:   = wb 1   ≤ wle 2  ⊥ wn 4   ≡ tb 5   ∪ wo 6   ∩ wa 7  1wt 8  0wf 9 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:  wwfh1  216  wwfh2  217
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