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Theorem u3lemnanb 657
Description: Lemma for Kalmbach implication study.
Assertion
Ref Expression
u3lemnanb ((a ->3 b)' ^ b') = (a ^ b')
Proof of Theorem u3lemnanb
StepHypRef Expression
1 u3lemob 632 . . 3 ((a ->3 b) v b) = (a' v b)
2 oran 87 . . 3 ((a ->3 b) v b) = ((a ->3 b)' ^ b')'
3 oran2 92 . . 3 (a' v b) = (a ^ b')'
41, 2, 33tr2 64 . 2 ((a ->3 b)' ^ b')' = (a ^ b')'
54con1 66 1 ((a ->3 b)' ^ b') = (a ^ b')
Colors of variables: term
Syntax hints:   = wb 1  'wn 4   v wo 6   ^ wa 7   ->3 wi3 14
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-i3 46  df-le1 130  df-le2 131  df-c1 132  df-c2 133
This theorem is referenced by:  u3lem3  751
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