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Theorem nom11 308
Description: Part of Lemma 3.3(14) from "Non-Orthomodular Models..." paper.
Assertion
Ref Expression
nom11 (a ->1 (a ^ b)) = (a ->1 b)
Proof of Theorem nom11
StepHypRef Expression
1 anass 76 . . . . 5 ((a ^ a) ^ b) = (a ^ (a ^ b))
21ax-r1 35 . . . 4 (a ^ (a ^ b)) = ((a ^ a) ^ b)
3 anidm 111 . . . . 5 (a ^ a) = a
43ran 78 . . . 4 ((a ^ a) ^ b) = (a ^ b)
52, 4ax-r2 36 . . 3 (a ^ (a ^ b)) = (a ^ b)
65lor 70 . 2 (a' v (a ^ (a ^ b))) = (a' v (a ^ b))
7 df-i1 44 . 2 (a ->1 (a ^ b)) = (a' v (a ^ (a ^ b)))
8 df-i1 44 . 2 (a ->1 b) = (a' v (a ^ b))
96, 7, 83tr1 63 1 (a ->1 (a ^ b)) = (a ->1 b)
Colors of variables: term
Syntax hints:   = wb 1  'wn 4   v wo 6   ^ wa 7   ->1 wi1 12
This theorem was proved from axioms:  ax-a1 30  ax-a2 31  ax-a3 32  ax-a5 34  ax-r1 35  ax-r2 36  ax-r4 37  ax-r5 38
This theorem depends on definitions:  df-a 40  df-t 41  df-f 42  df-i1 44
This theorem is referenced by:  nom42  327  lem3.3.7i1e3  1062
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