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Theorem u2lemnaa 641
Description: Lemma for Dishkant implication study.
Assertion
Ref Expression
u2lemnaa ((a ->2 b)' ^ a) = (a ^ b')
Proof of Theorem u2lemnaa
StepHypRef Expression
1 anor2 89 . . 3 ((a ->2 b)' ^ a) = ((a ->2 b) v a')'
2 u2lemona 626 . . . 4 ((a ->2 b) v a') = (a' v b)
32ax-r4 37 . . 3 ((a ->2 b) v a')' = (a' v b)'
41, 3ax-r2 36 . 2 ((a ->2 b)' ^ a) = (a' v b)'
5 anor1 88 . . 3 (a ^ b') = (a' v b)'
65ax-r1 35 . 2 (a' v b)' = (a ^ b')
74, 6ax-r2 36 1 ((a ->2 b)' ^ a) = (a ^ 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-i2 45  df-le1 130  df-le2 131
This theorem is referenced by:  u2lem7  773
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