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Theorem u1lemnanb 655
Description: Lemma for Sasaki implication study.
Assertion
Ref Expression
u1lemnanb ((a ->1 b)' ^ b') = (a ^ b')
Proof of Theorem u1lemnanb
StepHypRef Expression
1 u1lemob 630 . . 3 ((a ->1 b) v b) = (a' v b)
2 oran 87 . . 3 ((a ->1 b) v b) = ((a ->1 b)' ^ b')'
3 oran2 92 . . 3 (a' v b) = (a ^ b')'
41, 2, 33tr2 64 . 2 ((a ->1 b)' ^ b')' = (a ^ b')'
54con1 66 1 ((a ->1 b)' ^ b') = (a ^ b')
Colors of variables: term
Syntax hints:   = wb 1  'wn 4   v wo 6   ^ wa 7   ->1 wi1 12
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-i1 44  df-le1 130  df-le2 131
This theorem is referenced by:  u3lem14a  791
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