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Theorem nom45 330
Description: Part of Lemma 3.3(15) from "Non-Orthomodular Models..." paper.
Assertion
Ref Expression
nom45 ((a v b) ->5 b) = (a ->2 b)
Proof of Theorem nom45
StepHypRef Expression
1 ancom 74 . . . . . 6 (b' ^ a') = (a' ^ b')
2 anor3 90 . . . . . 6 (a' ^ b') = (a v b)'
31, 2ax-r2 36 . . . . 5 (b' ^ a') = (a v b)'
43ud5lem0a 264 . . . 4 (b' ->5 (b' ^ a')) = (b' ->5 (a v b)')
54ax-r1 35 . . 3 (b' ->5 (a v b)') = (b' ->5 (b' ^ a'))
6 nom15 312 . . 3 (b' ->5 (b' ^ a')) = (b' ->1 a')
75, 6ax-r2 36 . 2 (b' ->5 (a v b)') = (b' ->1 a')
8 i5con 272 . 2 ((a v b) ->5 b) = (b' ->5 (a v b)')
9 i2i1 267 . 2 (a ->2 b) = (b' ->1 a')
107, 8, 93tr1 63 1 ((a v b) ->5 b) = (a ->2 b)
Colors of variables: term
Syntax hints:   = wb 1  'wn 4   v wo 6   ^ wa 7   ->1 wi1 12   ->2 wi2 13   ->5 wi5 16
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  df-i2 45  df-i5 48  df-le1 130  df-le2 131
This theorem is referenced by: (None)
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