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Theorem nom12 309
Description: Part of Lemma 3.3(14) from "Non-Orthomodular Models..." paper.
Assertion
Ref Expression
nom12 (a ->2 (a ^ b)) = (a ->1 b)
Proof of Theorem nom12
StepHypRef Expression
1 oran 87 . . . . . . 7 (a v (a ^ b)) = (a' ^ (a ^ b)')'
21ax-r1 35 . . . . . 6 (a' ^ (a ^ b)')' = (a v (a ^ b))
3 orabs 120 . . . . . 6 (a v (a ^ b)) = a
42, 3ax-r2 36 . . . . 5 (a' ^ (a ^ b)')' = a
54con3 68 . . . 4 (a' ^ (a ^ b)') = a'
65lor 70 . . 3 ((a ^ b) v (a' ^ (a ^ b)')) = ((a ^ b) v a')
7 ax-a2 31 . . 3 ((a ^ b) v a') = (a' v (a ^ b))
86, 7ax-r2 36 . 2 ((a ^ b) v (a' ^ (a ^ b)')) = (a' v (a ^ b))
9 df-i2 45 . 2 (a ->2 (a ^ b)) = ((a ^ b) v (a' ^ (a ^ b)'))
10 df-i1 44 . 2 (a ->1 b) = (a' v (a ^ b))
118, 9, 103tr1 63 1 (a ->2 (a ^ b)) = (a ->1 b)
Colors of variables: term
Syntax hints:   = wb 1  'wn 4   v wo 6   ^ wa 7   ->1 wi1 12   ->2 wi2 13
This theorem was proved from axioms:  ax-a1 30  ax-a2 31  ax-a5 34  ax-r1 35  ax-r2 36  ax-r4 37  ax-r5 38
This theorem depends on definitions:  df-a 40  df-i1 44  df-i2 45
This theorem is referenced by:  nom41  326  lem3.3.7i2e3  1065
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