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Theorem nomcon0 301
Description: Lemma for "Non-Orthomodular Models..." paper.
Assertion
Ref Expression
nomcon0 (a ==0 b) = (b' ==0 a')
Proof of Theorem nomcon0
StepHypRef Expression
1 ax-a2 31 . . . 4 (a' v b) = (b v a')
2 ax-a1 30 . . . . 5 b = b''
32ax-r5 38 . . . 4 (b v a') = (b'' v a')
41, 3ax-r2 36 . . 3 (a' v b) = (b'' v a')
5 ax-a2 31 . . . 4 (b' v a) = (a v b')
6 ax-a1 30 . . . . 5 a = a''
76ax-r5 38 . . . 4 (a v b') = (a'' v b')
85, 7ax-r2 36 . . 3 (b' v a) = (a'' v b')
94, 82an 79 . 2 ((a' v b) ^ (b' v a)) = ((b'' v a') ^ (a'' v b'))
10 df-id0 49 . 2 (a ==0 b) = ((a' v b) ^ (b' v a))
11 df-id0 49 . 2 (b' ==0 a') = ((b'' v a') ^ (a'' v b'))
129, 10, 113tr1 63 1 (a ==0 b) = (b' ==0 a')
Colors of variables: term
Syntax hints:   = wb 1  'wn 4   v wo 6   ^ wa 7   ==0 wid0 17
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-id0 49
This theorem is referenced by:  nom50  331
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