QLE Home Quantum Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  QLE Home  >  Th. List  >  ud4lem3a Unicode version
Theorem ud4lem3a 583
Description: Lemma for unified disjunction.
Assertion
Ref Expression
ud4lem3a ((a ->4 b)' ^ (a v b)) = (a ->4 b)'
Proof of Theorem ud4lem3a
StepHypRef Expression
1 anass 76 . . 3 ((((a' v b') ^ (a v b')) ^ ((a ^ b') v b)) ^ (a v b)) = (((a' v b') ^ (a v b')) ^ (((a ^ b') v b) ^ (a v b)))
2 lea 160 . . . . . 6 (a ^ b') =< a
32leror 152 . . . . 5 ((a ^ b') v b) =< (a v b)
43df2le2 136 . . . 4 (((a ^ b') v b) ^ (a v b)) = ((a ^ b') v b)
54lan 77 . . 3 (((a' v b') ^ (a v b')) ^ (((a ^ b') v b) ^ (a v b))) = (((a' v b') ^ (a v b')) ^ ((a ^ b') v b))
61, 5ax-r2 36 . 2 ((((a' v b') ^ (a v b')) ^ ((a ^ b') v b)) ^ (a v b)) = (((a' v b') ^ (a v b')) ^ ((a ^ b') v b))
7 ud4lem0c 280 . . 3 (a ->4 b)' = (((a' v b') ^ (a v b')) ^ ((a ^ b') v b))
87ran 78 . 2 ((a ->4 b)' ^ (a v b)) = ((((a' v b') ^ (a v b')) ^ ((a ^ b') v b)) ^ (a v b))
96, 8, 73tr1 63 1 ((a ->4 b)' ^ (a v b)) = (a ->4 b)'
Colors of variables: term
Syntax hints:   = wb 1  'wn 4   v wo 6   ^ wa 7   ->4 wi4 15
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-i4 47  df-le1 130  df-le2 131
This theorem is referenced by:  ud4lem3  585
  Copyright terms: Public domain W3C validator