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Theorem woml 211
Description: Theorem structurally similar to orthomodular law but does not require R3. (Contributed by NM, 2-Sep-1997.)
Assertion
Ref Expression
woml ((a ∪ (a ∩ (ab))) ≡ (ab)) = 1

Proof of Theorem woml
StepHypRef Expression
1 omlem1 127 . 2 ((a ∪ (a ∩ (ab))) ∪ (ab)) = (ab)
2 omlem2 128 . 2 ((ab) ∪ (a ∪ (a ∩ (ab)))) = 1
31, 2wlem3.1 210 1 ((a ∪ (a ∩ (ab))) ≡ (ab)) = 1
Colors of variables: term
Syntax hints:   = wb 1   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
This theorem is referenced by:  wwoml2  212  ska11  239  wom4  380
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