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Theorem nomcon2 303
 Description: Lemma for "Non-Orthomodular Models..." paper.
Assertion
Ref Expression
nomcon2 (a2 b) = (b1 a )

Proof of Theorem nomcon2
StepHypRef Expression
1 ax-a2 31 . . . 4 (ab ) = (ba)
2 ax-a1 30 . . . . 5 a = a
32lor 70 . . . 4 (ba) = (ba )
41, 3ax-r2 36 . . 3 (ab ) = (ba )
5 ax-a1 30 . . . 4 b = b
6 ancom 74 . . . 4 (ab ) = (ba )
75, 62or 72 . . 3 (b ∪ (ab )) = (b ∪ (ba ))
84, 72an 79 . 2 ((ab ) ∩ (b ∪ (ab ))) = ((ba ) ∩ (b ∪ (ba )))
9 df-id2 51 . 2 (a2 b) = ((ab ) ∩ (b ∪ (ab )))
10 df-id1 50 . 2 (b1 a ) = ((ba ) ∩ (b ∪ (ba )))
118, 9, 103tr1 63 1 (a2 b) = (b1 a )
 Colors of variables: term Syntax hints:   = wb 1  ⊥ wn 4   ∪ wo 6   ∩ wa 7   ≡1 wid1 18   ≡2 wid2 19 This theorem was proved from axioms:  ax-a1 30  ax-a2 31  ax-r1 35  ax-r2 36  ax-r4 37  ax-r5 38 This theorem depends on definitions:  df-a 40  df-id1 50  df-id2 51 This theorem is referenced by:  nomcon3  304  nom52  333
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