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Theorem nomb41 299
Description: Lemma for "Non-Orthomodular Models..." paper.
Assertion
Ref Expression
nomb41 (a ==4 b) = (b ==1 a)
Proof of Theorem nomb41
StepHypRef Expression
1 ax-a2 31 . . 3 (a' v b) = (b v a')
2 ancom 74 . . . 4 (a ^ b) = (b ^ a)
32lor 70 . . 3 (b' v (a ^ b)) = (b' v (b ^ a))
41, 32an 79 . 2 ((a' v b) ^ (b' v (a ^ b))) = ((b v a') ^ (b' v (b ^ a)))
5 df-id4 53 . 2 (a ==4 b) = ((a' v b) ^ (b' v (a ^ b)))
6 df-id1 50 . 2 (b ==1 a) = ((b v a') ^ (b' v (b ^ a)))
74, 5, 63tr1 63 1 (a ==4 b) = (b ==1 a)
Colors of variables: term
Syntax hints:   = wb 1  'wn 4   v wo 6   ^ wa 7   ==1 wid1 18   ==4 wid4 21
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-id1 50  df-id4 53
This theorem is referenced by:  nomcon3  304  nomcon4  305  nom31  320  nom34  323  nom61  338  nom64  341
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