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Theorem u2lemob 631
Description: Lemma for Dishkant implication study.
Assertion
Ref Expression
u2lemob ((a ->2 b) v b) = ((a' ^ b') v b)
Proof of Theorem u2lemob
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 oridm 110 . . . . 5 (b v b) = b
65lor 70 . . . 4 ((a' ^ b') v (b v b)) = ((a' ^ b') v b)
74, 6ax-r2 36 . . 3 ((b v b) v (a' ^ b')) = ((a' ^ b') v b)
83, 7ax-r2 36 . 2 ((b v (a' ^ b')) v b) = ((a' ^ b') v b)
92, 8ax-r2 36 1 ((a ->2 b) v b) = ((a' ^ b') v b)
Colors of variables: term
Syntax hints:   = wb 1  'wn 4   v wo 6   ^ wa 7   ->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-t 41  df-f 42  df-i2 45
This theorem is referenced by:  u2lemnanb  656
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