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Theorem wom5 381
 Description: Orthomodular law. Kalmbach 83 p. 22.
Hypotheses
Ref Expression
wom5.1 (a2 b) = 1
wom5.2 ((ba ) ≡ 0) = 1
Assertion
Ref Expression
wom5 (ab) = 1

Proof of Theorem wom5
StepHypRef Expression
1 wom5.2 . . . . 5 ((ba ) ≡ 0) = 1
21wr1 197 . . . 4 (0 ≡ (ba )) = 1
3 ancom 74 . . . . 5 (ba ) = (ab)
43bi1 118 . . . 4 ((ba ) ≡ (ab)) = 1
52, 4wr2 371 . . 3 (0 ≡ (ab)) = 1
65wlor 368 . 2 ((a ∪ 0) ≡ (a ∪ (ab))) = 1
7 or0 102 . . 3 (a ∪ 0) = a
87bi1 118 . 2 ((a ∪ 0) ≡ a) = 1
9 wom5.1 . . 3 (a2 b) = 1
109wom4 380 . 2 ((a ∪ (ab)) ≡ b) = 1
116, 8, 10w3tr2 375 1 (ab) = 1
 Colors of variables: term Syntax hints:   = wb 1  ⊥ wn 4   ≡ tb 5   ∪ wo 6   ∩ wa 7  1wt 8  0wf 9   ≤2 wle2 10 This theorem was proved from axioms:  ax-a1 30  ax-a2 31  ax-a3 32  ax-a4 33  ax-a5 34  ax-r1 35  ax-r2 36  ax-r4 37  ax-r5 38  ax-wom 361 This theorem depends on definitions:  df-b 39  df-a 40  df-t 41  df-f 42  df-i1 44  df-i2 45  df-le 129  df-le1 130  df-le2 131 This theorem is referenced by:  wfh1  423  wfh2  424
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