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Theorem nomb32 300
 Description: Lemma for "Non-Orthomodular Models..." paper.
Assertion
Ref Expression
nomb32 (a3 b) = (b2 a)

Proof of Theorem nomb32
StepHypRef Expression
1 ax-a2 31 . . 3 (ab) = (ba )
2 ancom 74 . . . 4 (ab ) = (ba )
32lor 70 . . 3 (a ∪ (ab )) = (a ∪ (ba ))
41, 32an 79 . 2 ((ab) ∩ (a ∪ (ab ))) = ((ba ) ∩ (a ∪ (ba )))
5 df-id3 52 . 2 (a3 b) = ((ab) ∩ (a ∪ (ab )))
6 df-id2 51 . 2 (b2 a) = ((ba ) ∩ (a ∪ (ba )))
74, 5, 63tr1 63 1 (a3 b) = (b2 a)
 Colors of variables: term Syntax hints:   = wb 1  ⊥ wn 4   ∪ wo 6   ∩ wa 7   ≡2 wid2 19   ≡3 wid3 20 This theorem was proved from axioms:  ax-a2 31  ax-r1 35  ax-r2 36  ax-r4 37  ax-r5 38 This theorem depends on definitions:  df-a 40  df-id2 51  df-id3 52 This theorem is referenced by:  nomcon3  304  nomcon4  305  nom32  321  nom33  322  nom62  339  nom63  340
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