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Theorem nom55 336
Description: Part of Lemma 3.3(15) from "Non-Orthomodular Models..." paper.
Assertion
Ref Expression
nom55 ((a v b) == b) = (a ->2 b)
Proof of Theorem nom55
StepHypRef Expression
1 nom25 318 . 2 (b' == (b' ^ a')) = (b' ->1 a')
2 conb 122 . . 3 ((a v b) == b) = ((a v b)' == b')
3 bicom 96 . . 3 ((a v b)' == b') = (b' == (a v b)')
4 ancom 74 . . . . . 6 (b' ^ a') = (a' ^ b')
5 anor3 90 . . . . . 6 (a' ^ b') = (a v b)'
64, 5ax-r2 36 . . . . 5 (b' ^ a') = (a v b)'
76ax-r1 35 . . . 4 (a v b)' = (b' ^ a')
87lbi 97 . . 3 (b' == (a v b)') = (b' == (b' ^ a'))
92, 3, 83tr 65 . 2 ((a v b) == b) = (b' == (b' ^ a'))
10 i2i1 267 . 2 (a ->2 b) = (b' ->1 a')
111, 9, 103tr1 63 1 ((a v b) == b) = (a ->2 b)
Colors of variables: term
Syntax hints:   = wb 1  'wn 4   == tb 5   v wo 6   ^ wa 7   ->1 wi1 12   ->2 wi2 13
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-b 39  df-a 40  df-t 41  df-f 42  df-i1 44  df-i2 45
This theorem is referenced by:  nom65  342
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