QLE Home Quantum Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  QLE Home  >  Th. List  >  wql2lem Unicode version
Theorem wql2lem 288
Description: Classical implication inferred from Dishkant implication.
Hypothesis
Ref Expression
wql2lem.1 (a ->2 b) = 1
Assertion
Ref Expression
wql2lem (a' v b) = 1
Proof of Theorem wql2lem
StepHypRef Expression
1 le1 146 . 2 (a' v b) =< 1
2 df-i2 45 . . . 4 (a ->2 b) = (b v (a' ^ b'))
3 wql2lem.1 . . . 4 (a ->2 b) = 1
4 ax-a2 31 . . . 4 (b v (a' ^ b')) = ((a' ^ b') v b)
52, 3, 43tr2 64 . . 3 1 = ((a' ^ b') v b)
6 lea 160 . . . 4 (a' ^ b') =< a'
76leror 152 . . 3 ((a' ^ b') v b) =< (a' v b)
85, 7bltr 138 . 2 1 =< (a' v b)
91, 8lebi 145 1 (a' v b) = 1
Colors of variables: term
Syntax hints:   = wb 1  'wn 4   v wo 6   ^ wa 7  1wt 8   ->2 wi2 13
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
This theorem depends on definitions:  df-a 40  df-t 41  df-f 42  df-i2 45  df-le1 130  df-le2 131
This theorem is referenced by:  wql2lem3  290
  Copyright terms: Public domain W3C validator