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Theorem nom12 309
 Description: Part of Lemma 3.3(14) from "Non-Orthomodular Models..." paper.
Assertion
Ref Expression
nom12 (a2 (ab)) = (a1 b)

Proof of Theorem nom12
StepHypRef Expression
1 oran 87 . . . . . . 7 (a ∪ (ab)) = (a ∩ (ab) )
21ax-r1 35 . . . . . 6 (a ∩ (ab) ) = (a ∪ (ab))
3 orabs 120 . . . . . 6 (a ∪ (ab)) = a
42, 3ax-r2 36 . . . . 5 (a ∩ (ab) ) = a
54con3 68 . . . 4 (a ∩ (ab) ) = a
65lor 70 . . 3 ((ab) ∪ (a ∩ (ab) )) = ((ab) ∪ a )
7 ax-a2 31 . . 3 ((ab) ∪ a ) = (a ∪ (ab))
86, 7ax-r2 36 . 2 ((ab) ∪ (a ∩ (ab) )) = (a ∪ (ab))
9 df-i2 45 . 2 (a2 (ab)) = ((ab) ∪ (a ∩ (ab) ))
10 df-i1 44 . 2 (a1 b) = (a ∪ (ab))
118, 9, 103tr1 63 1 (a2 (ab)) = (a1 b)
 Colors of variables: term Syntax hints:   = wb 1  ⊥ wn 4   ∪ wo 6   ∩ wa 7   →1 wi1 12   →2 wi2 13 This theorem was proved from axioms:  ax-a1 30  ax-a2 31  ax-a5 34  ax-r1 35  ax-r2 36  ax-r4 37  ax-r5 38 This theorem depends on definitions:  df-a 40  df-i1 44  df-i2 45 This theorem is referenced by:  nom41  326  lem3.3.7i2e3  1065
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