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Theorem nomcon1 302
 Description: Lemma for "Non-Orthomodular Models..." paper.
Assertion
Ref Expression
nomcon1 (a1 b) = (b2 a )

Proof of Theorem nomcon1
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 ancom 74 . . . . 5 (ab) = (ba)
6 ax-a1 30 . . . . . 6 b = b
76, 22an 79 . . . . 5 (ba) = (b a )
85, 7ax-r2 36 . . . 4 (ab) = (b a )
98lor 70 . . 3 (a ∪ (ab)) = (a ∪ (b a ))
104, 92an 79 . 2 ((ab ) ∩ (a ∪ (ab))) = ((ba ) ∩ (a ∪ (b a )))
11 df-id1 50 . 2 (a1 b) = ((ab ) ∩ (a ∪ (ab)))
12 df-id2 51 . 2 (b2 a ) = ((ba ) ∩ (a ∪ (b a )))
1310, 11, 123tr1 63 1 (a1 b) = (b2 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:  nomcon4  305  nom51  332
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