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Theorem u2lemnanb 656
Description: Lemma for Dishkant implication study.
Assertion
Ref Expression
u2lemnanb ((a ->2 b)' ^ b') = ((a v b) ^ b')
Proof of Theorem u2lemnanb
StepHypRef Expression
1 u2lemob 631 . . . 4 ((a ->2 b) v b) = ((a' ^ b') v b)
2 anor3 90 . . . . 5 (a' ^ b') = (a v b)'
32ax-r5 38 . . . 4 ((a' ^ b') v b) = ((a v b)' v b)
41, 3ax-r2 36 . . 3 ((a ->2 b) v b) = ((a v b)' v b)
5 oran 87 . . 3 ((a ->2 b) v b) = ((a ->2 b)' ^ b')'
6 oran2 92 . . 3 ((a v b)' v b) = ((a v b) ^ b')'
74, 5, 63tr2 64 . 2 ((a ->2 b)' ^ b')' = ((a v b) ^ b')'
87con1 66 1 ((a ->2 b)' ^ b') = ((a v b) ^ 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-a 40  df-t 41  df-f 42  df-i2 45
This theorem is referenced by: (None)
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