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Theorem nom40 325
 Description: Part of Lemma 3.3(15) from "Non-Orthomodular Models..." paper.
Assertion
Ref Expression
nom40 ((ab) →0 b) = (a2 b)

Proof of Theorem nom40
StepHypRef Expression
1 nom10 307 . 2 (b0 (ba )) = (b1 a )
2 ax-a2 31 . . . 4 ((ab)b) = (b ∪ (ab) )
3 ax-a1 30 . . . . 5 b = b
4 ancom 74 . . . . . . 7 (ba ) = (ab )
5 anor3 90 . . . . . . 7 (ab ) = (ab)
64, 5ax-r2 36 . . . . . 6 (ba ) = (ab)
76ax-r1 35 . . . . 5 (ab) = (ba )
83, 72or 72 . . . 4 (b ∪ (ab) ) = (b ∪ (ba ))
92, 8ax-r2 36 . . 3 ((ab)b) = (b ∪ (ba ))
10 df-i0 43 . . 3 ((ab) →0 b) = ((ab)b)
11 df-i0 43 . . 3 (b0 (ba )) = (b ∪ (ba ))
129, 10, 113tr1 63 . 2 ((ab) →0 b) = (b0 (ba ))
13 i2i1 267 . 2 (a2 b) = (b1 a )
141, 12, 133tr1 63 1 ((ab) →0 b) = (a2 b)
 Colors of variables: term Syntax hints:   = wb 1  ⊥ wn 4   ∪ wo 6   ∩ wa 7   →0 wi0 11   →1 wi1 12   →2 wi2 13 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-i0 43  df-i1 44  df-i2 45 This theorem is referenced by: (None)
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