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Theorem u4lemnob 673
Description: Lemma for non-tollens implication study.
Assertion
Ref Expression
u4lemnob ((a ->4 b)' v b) = ((a ^ b') v b)
Proof of Theorem u4lemnob
StepHypRef Expression
1 u4lemanb 618 . . . 4 ((a ->4 b) ^ b') = ((a' v b) ^ b')
2 oran2 92 . . . . 5 (a' v b) = (a ^ b')'
32ran 78 . . . 4 ((a' v b) ^ b') = ((a ^ b')' ^ b')
41, 3ax-r2 36 . . 3 ((a ->4 b) ^ b') = ((a ^ b')' ^ b')
5 anor1 88 . . 3 ((a ->4 b) ^ b') = ((a ->4 b)' v b)'
6 anor3 90 . . 3 ((a ^ b')' ^ b') = ((a ^ b') v b)'
74, 5, 63tr2 64 . 2 ((a ->4 b)' v b)' = ((a ^ b') v b)'
87con1 66 1 ((a ->4 b)' v b) = ((a ^ b') v b)
Colors of variables: term
Syntax hints:   = wb 1  'wn 4   v wo 6   ^ wa 7   ->4 wi4 15
This theorem was proved from axioms:  ax-a1 30  ax-a2 31  ax-a3 32  ax-a4 33  ax-a5 34  ax-r1 35  ax-r2 36  ax-r4 37  ax-r5 38  ax-r3 439
This theorem depends on definitions:  df-b 39  df-a 40  df-t 41  df-f 42  df-i4 47  df-le1 130  df-le2 131  df-c1 132  df-c2 133
This theorem is referenced by: (None)
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