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Theorem u2lemoa 621
Description: Lemma for Dishkant implication study.
Assertion
Ref Expression
u2lemoa ((a ->2 b) v a) = 1
Proof of Theorem u2lemoa
StepHypRef Expression
1 df-i2 45 . . 3 (a ->2 b) = (b v (a' ^ b'))
21ax-r5 38 . 2 ((a ->2 b) v a) = ((b v (a' ^ b')) v a)
3 ax-a2 31 . . 3 ((b v (a' ^ b')) v a) = (a v (b v (a' ^ b')))
4 ax-a3 32 . . . . 5 ((a v b) v (a' ^ b')) = (a v (b v (a' ^ b')))
54ax-r1 35 . . . 4 (a v (b v (a' ^ b'))) = ((a v b) v (a' ^ b'))
6 ax-a2 31 . . . . 5 ((a v b) v (a' ^ b')) = ((a' ^ b') v (a v b))
7 oran 87 . . . . . . 7 (a v b) = (a' ^ b')'
87lor 70 . . . . . 6 ((a' ^ b') v (a v b)) = ((a' ^ b') v (a' ^ b')')
9 df-t 41 . . . . . . 7 1 = ((a' ^ b') v (a' ^ b')')
109ax-r1 35 . . . . . 6 ((a' ^ b') v (a' ^ b')') = 1
118, 10ax-r2 36 . . . . 5 ((a' ^ b') v (a v b)) = 1
126, 11ax-r2 36 . . . 4 ((a v b) v (a' ^ b')) = 1
135, 12ax-r2 36 . . 3 (a v (b v (a' ^ b'))) = 1
143, 13ax-r2 36 . 2 ((b v (a' ^ b')) v a) = 1
152, 14ax-r2 36 1 ((a ->2 b) v a) = 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-a1 30  ax-a2 31  ax-a3 32  ax-r1 35  ax-r2 36  ax-r4 37  ax-r5 38
This theorem depends on definitions:  df-a 40  df-t 41  df-i2 45
This theorem is referenced by:  u2lemnana  646
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