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Theorem wom4 380
 Description: Orthomodular law. Kalmbach 83 p. 22.
Hypothesis
Ref Expression
wom4.1 (a2 b) = 1
Assertion
Ref Expression
wom4 ((a ∪ (ab)) ≡ b) = 1

Proof of Theorem wom4
StepHypRef Expression
1 woml 211 . 2 ((a ∪ (a ∩ (ab))) ≡ (ab)) = 1
2 wom4.1 . . . . 5 (a2 b) = 1
32wdf-le2 379 . . . 4 ((ab) ≡ b) = 1
43wlan 370 . . 3 ((a ∩ (ab)) ≡ (ab)) = 1
54wlor 368 . 2 ((a ∪ (a ∩ (ab))) ≡ (a ∪ (ab))) = 1
61, 5, 3w3tr2 375 1 ((a ∪ (ab)) ≡ b) = 1
 Colors of variables: term Syntax hints:   = wb 1  ⊥ wn 4   ≡ tb 5   ∪ wo 6   ∩ wa 7  1wt 8   ≤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:  wom5  381  wcomlem  382  wcom3i  422
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