QLE Home Quantum Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  QLE Home  >  Th. List  >  wql1lem Unicode version
Theorem wql1lem 287
Description: Classical implication inferred from Sakaki implication.
Hypothesis
Ref Expression
wql1lem.1 (a ->1 b) = 1
Assertion
Ref Expression
wql1lem (a' v b) = 1
Proof of Theorem wql1lem
StepHypRef Expression
1 le1 146 . 2 (a' v b) =< 1
2 wql1lem.1 . . . 4 (a ->1 b) = 1
32ax-r1 35 . . 3 1 = (a ->1 b)
4 df-i1 44 . . . 4 (a ->1 b) = (a' v (a ^ b))
5 lear 161 . . . . 5 (a ^ b) =< b
65lelor 166 . . . 4 (a' v (a ^ b)) =< (a' v b)
74, 6bltr 138 . . 3 (a ->1 b) =< (a' v b)
83, 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   ->1 wi1 12
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-i1 44  df-le1 130  df-le2 131
This theorem is referenced by:  wql1  293  wdwom  1104
  Copyright terms: Public domain W3C validator