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Theorem omlem2 128
 Description: Lemma in proof of Th. 1 of Pavicic 1987.
Assertion
Ref Expression
omlem2 ((ab) ∪ (a ∪ (a ∩ (ab)))) = 1

Proof of Theorem omlem2
StepHypRef Expression
1 ax-a2 31 . . 3 ((ab)a) = (a ∪ (ab) )
2 anor2 89 . . 3 (a ∩ (ab)) = (a ∪ (ab) )
31, 22or 72 . 2 (((ab)a) ∪ (a ∩ (ab))) = ((a ∪ (ab) ) ∪ (a ∪ (ab) ) )
4 ax-a3 32 . . 3 (((ab)a) ∪ (a ∩ (ab))) = ((ab) ∪ (a ∪ (a ∩ (ab))))
54ax-r1 35 . 2 ((ab) ∪ (a ∪ (a ∩ (ab)))) = (((ab)a) ∪ (a ∩ (ab)))
6 df-t 41 . 2 1 = ((a ∪ (ab) ) ∪ (a ∪ (ab) ) )
73, 5, 63tr1 63 1 ((ab) ∪ (a ∪ (a ∩ (ab)))) = 1
 Colors of variables: term Syntax hints:   = wb 1  ⊥ wn 4   ∪ wo 6   ∩ wa 7  1wt 8 This theorem was proved from axioms:  ax-a1 30  ax-a2 31  ax-a3 32  ax-r1 35  ax-r2 36  ax-r4 37  ax-r5 38 This theorem depends on definitions:  df-a 40  df-t 41 This theorem is referenced by:  woml  211  wql2lem3  290  oml  445
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