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Theorem nomcon1 302
Description: Lemma for "Non-Orthomodular Models..." paper.
Assertion
Ref Expression
nomcon1 (a ==1 b) = (b' ==2 a')
Proof of Theorem nomcon1
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 ancom 74 . . . . 5 (a ^ b) = (b ^ a)
6 ax-a1 30 . . . . . 6 b = b''
76, 22an 79 . . . . 5 (b ^ a) = (b'' ^ a'')
85, 7ax-r2 36 . . . 4 (a ^ b) = (b'' ^ a'')
98lor 70 . . 3 (a' v (a ^ b)) = (a' v (b'' ^ a''))
104, 92an 79 . 2 ((a v b') ^ (a' v (a ^ b))) = ((b' v a'') ^ (a' v (b'' ^ a'')))
11 df-id1 50 . 2 (a ==1 b) = ((a v b') ^ (a' v (a ^ b)))
12 df-id2 51 . 2 (b' ==2 a') = ((b' v a'') ^ (a' v (b'' ^ a'')))
1310, 11, 123tr1 63 1 (a ==1 b) = (b' ==2 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:  nomcon4  305  nom51  332
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