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Theorem u3lemnaa 642
Description: Lemma for Kalmbach implication study.
Assertion
Ref Expression
u3lemnaa ((a ->3 b)' ^ a) = (a ^ b')
Proof of Theorem u3lemnaa
StepHypRef Expression
1 anor2 89 . 2 ((a ->3 b)' ^ a) = ((a ->3 b) v a')'
2 anor1 88 . . . 4 (a ^ b') = (a' v b)'
3 u3lemona 627 . . . . . 6 ((a ->3 b) v a') = (a' v b)
43ax-r4 37 . . . . 5 ((a ->3 b) v a')' = (a' v b)'
54ax-r1 35 . . . 4 (a' v b)' = ((a ->3 b) v a')'
62, 5ax-r2 36 . . 3 (a ^ b') = ((a ->3 b) v a')'
76ax-r1 35 . 2 ((a ->3 b) v a')' = (a ^ b')
81, 7ax-r2 36 1 ((a ->3 b)' ^ a) = (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-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
This theorem is referenced by:  u3lem13a  789  u3lem13b  790
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