QLE Home Quantum Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  QLE Home  >  Th. List  >  u5lemnaa Unicode version
Theorem u5lemnaa 644
Description: Lemma for relevance implication study.
Assertion
Ref Expression
u5lemnaa ((a ->5 b)' ^ a) = (a ^ (a' v b'))
Proof of Theorem u5lemnaa
StepHypRef Expression
1 anor2 89 . 2 ((a ->5 b)' ^ a) = ((a ->5 b) v a')'
2 u5lemona 629 . . . 4 ((a ->5 b) v a') = (a' v (a ^ b))
32ax-r4 37 . . 3 ((a ->5 b) v a')' = (a' v (a ^ b))'
4 anor1 88 . . . . 5 (a ^ (a ^ b)') = (a' v (a ^ b))'
54ax-r1 35 . . . 4 (a' v (a ^ b))' = (a ^ (a ^ b)')
6 df-a 40 . . . . . 6 (a ^ b) = (a' v b')'
76con2 67 . . . . 5 (a ^ b)' = (a' v b')
87lan 77 . . . 4 (a ^ (a ^ b)') = (a ^ (a' v b'))
95, 8ax-r2 36 . . 3 (a' v (a ^ b))' = (a ^ (a' v b'))
103, 9ax-r2 36 . 2 ((a ->5 b) v a')' = (a ^ (a' v b'))
111, 10ax-r2 36 1 ((a ->5 b)' ^ a) = (a ^ (a' v b'))
Colors of variables: term
Syntax hints:   = wb 1  'wn 4   v wo 6   ^ wa 7   ->5 wi5 16
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-t 41  df-f 42  df-i5 48  df-le1 130  df-le2 131
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator