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Theorem nomcon2 303
Description: Lemma for "Non-Orthomodular Models..." paper.
Assertion
Ref Expression
nomcon2 (a ==2 b) = (b' ==1 a')
Proof of Theorem nomcon2
StepHypRef Expression
1 ax-a2 31 . . . 4 (a v b') = (b' v a)
2 ax-a1 30 . . . . 5 a = a''
32lor 70 . . . 4 (b' v a) = (b' v a'')
41, 3ax-r2 36 . . 3 (a v b') = (b' v a'')
5 ax-a1 30 . . . 4 b = b''
6 ancom 74 . . . 4 (a' ^ b') = (b' ^ a')
75, 62or 72 . . 3 (b v (a' ^ b')) = (b'' v (b' ^ a'))
84, 72an 79 . 2 ((a v b') ^ (b v (a' ^ b'))) = ((b' v a'') ^ (b'' v (b' ^ a')))
9 df-id2 51 . 2 (a ==2 b) = ((a v b') ^ (b v (a' ^ b')))
10 df-id1 50 . 2 (b' ==1 a') = ((b' v a'') ^ (b'' v (b' ^ a')))
118, 9, 103tr1 63 1 (a ==2 b) = (b' ==1 a')
Colors of variables: term
Syntax hints:   = wb 1  'wn 4   v 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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