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Theorem nom40 325
Description: Part of Lemma 3.3(15) from "Non-Orthomodular Models..." paper.
Assertion
Ref Expression
nom40 ((a v b) ->0 b) = (a ->2 b)

Proof of Theorem nom40
StepHypRef Expression
1 nom10 307 . 2 (b' ->0 (b' ^ a')) = (b' ->1 a')
2 ax-a2 31 . . . 4 ((a v b)' v b) = (b v (a v b)')
3 ax-a1 30 . . . . 5 b = b''
4 ancom 74 . . . . . . 7 (b' ^ a') = (a' ^ b')
5 anor3 90 . . . . . . 7 (a' ^ b') = (a v b)'
64, 5ax-r2 36 . . . . . 6 (b' ^ a') = (a v b)'
76ax-r1 35 . . . . 5 (a v b)' = (b' ^ a')
83, 72or 72 . . . 4 (b v (a v b)') = (b'' v (b' ^ a'))
92, 8ax-r2 36 . . 3 ((a v b)' v b) = (b'' v (b' ^ a'))
10 df-i0 43 . . 3 ((a v b) ->0 b) = ((a v b)' v b)
11 df-i0 43 . . 3 (b' ->0 (b' ^ a')) = (b'' v (b' ^ a'))
129, 10, 113tr1 63 . 2 ((a v b) ->0 b) = (b' ->0 (b' ^ a'))
13 i2i1 267 . 2 (a ->2 b) = (b' ->1 a')
141, 12, 133tr1 63 1 ((a v b) ->0 b) = (a ->2 b)
Colors of variables: term
Syntax hints:   = wb 1  'wn 4   v wo 6   ^ wa 7   ->0 wi0 11   ->1 wi1 12   ->2 wi2 13
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-i0 43  df-i1 44  df-i2 45
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