QLE Home Quantum Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  QLE Home  >  Th. List  >  womle3b Unicode version
Theorem womle3b 297
Description: Implied by the WOM law.
Hypothesis
Ref Expression
womle3b.1 ((a ->1 b)' v (a ->2 b)) = 1
Assertion
Ref Expression
womle3b (a ^ (a ->1 b)) =< ((a ->1 b)' v (a ->2 b))
Proof of Theorem womle3b
StepHypRef Expression
1 le1 146 . 2 (a ^ (a ->1 b)) =< 1
2 womle3b.1 . . 3 ((a ->1 b)' v (a ->2 b)) = 1
32ax-r1 35 . 2 1 = ((a ->1 b)' v (a ->2 b))
41, 3lbtr 139 1 (a ^ (a ->1 b)) =< ((a ->1 b)' v (a ->2 b))
Colors of variables: term
Syntax hints:   = wb 1   =< wle 2  'wn 4   v wo 6   ^ wa 7  1wt 8   ->1 wi1 12   ->2 wi2 13
This theorem was proved from axioms:  ax-a1 30  ax-a2 31  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-le1 130  df-le2 131
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator