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Theorem u2lemonb 636
Description: Lemma for Dishkant implication study.
Assertion
Ref Expression
u2lemonb ((a ->2 b) v b') = 1
Proof of Theorem u2lemonb
StepHypRef Expression
1 df-i2 45 . . 3 (a ->2 b) = (b v (a' ^ b'))
21ax-r5 38 . 2 ((a ->2 b) v b') = ((b v (a' ^ b')) v b')
3 or32 82 . . 3 ((b v (a' ^ b')) v b') = ((b v b') v (a' ^ b'))
4 ax-a2 31 . . . 4 ((b v b') v (a' ^ b')) = ((a' ^ b') v (b v b'))
5 df-t 41 . . . . . . 7 1 = (b v b')
65lor 70 . . . . . 6 ((a' ^ b') v 1) = ((a' ^ b') v (b v b'))
76ax-r1 35 . . . . 5 ((a' ^ b') v (b v b')) = ((a' ^ b') v 1)
8 or1 104 . . . . 5 ((a' ^ b') v 1) = 1
97, 8ax-r2 36 . . . 4 ((a' ^ b') v (b v b')) = 1
104, 9ax-r2 36 . . 3 ((b v b') v (a' ^ b')) = 1
113, 10ax-r2 36 . 2 ((b v (a' ^ b')) v b') = 1
122, 11ax-r2 36 1 ((a ->2 b) v b') = 1
Colors of variables: term
Syntax hints:   = wb 1  'wn 4   v wo 6   ^ wa 7  1wt 8   ->2 wi2 13
This theorem was proved from axioms:  ax-a2 31  ax-a3 32  ax-a4 33  ax-r1 35  ax-r2 36  ax-r5 38
This theorem depends on definitions:  df-t 41  df-i2 45
This theorem is referenced by:  u2lemnab  651  u2lem3  750  oa23  936
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