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Theorem nom11 308
 Description: Part of Lemma 3.3(14) from "Non-Orthomodular Models..." paper.
Assertion
Ref Expression
nom11 (a1 (ab)) = (a1 b)

Proof of Theorem nom11
StepHypRef Expression
1 anass 76 . . . . 5 ((aa) ∩ b) = (a ∩ (ab))
21ax-r1 35 . . . 4 (a ∩ (ab)) = ((aa) ∩ b)
3 anidm 111 . . . . 5 (aa) = a
43ran 78 . . . 4 ((aa) ∩ b) = (ab)
52, 4ax-r2 36 . . 3 (a ∩ (ab)) = (ab)
65lor 70 . 2 (a ∪ (a ∩ (ab))) = (a ∪ (ab))
7 df-i1 44 . 2 (a1 (ab)) = (a ∪ (a ∩ (ab)))
8 df-i1 44 . 2 (a1 b) = (a ∪ (ab))
96, 7, 83tr1 63 1 (a1 (ab)) = (a1 b)
 Colors of variables: term Syntax hints:   = wb 1  ⊥ wn 4   ∪ wo 6   ∩ wa 7   →1 wi1 12 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-a 40  df-t 41  df-f 42  df-i1 44 This theorem is referenced by:  nom42  327  lem3.3.7i1e3  1062
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