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Theorem nomb32 300
Description: Lemma for "Non-Orthomodular Models..." paper.
Assertion
Ref Expression
nomb32 (a ==3 b) = (b ==2 a)
Proof of Theorem nomb32
StepHypRef Expression
1 ax-a2 31 . . 3 (a' v b) = (b v a')
2 ancom 74 . . . 4 (a' ^ b') = (b' ^ a')
32lor 70 . . 3 (a v (a' ^ b')) = (a v (b' ^ a'))
41, 32an 79 . 2 ((a' v b) ^ (a v (a' ^ b'))) = ((b v a') ^ (a v (b' ^ a')))
5 df-id3 52 . 2 (a ==3 b) = ((a' v b) ^ (a v (a' ^ b')))
6 df-id2 51 . 2 (b ==2 a) = ((b v a') ^ (a v (b' ^ a')))
74, 5, 63tr1 63 1 (a ==3 b) = (b ==2 a)
Colors of variables: term
Syntax hints:   = wb 1  'wn 4   v 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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