QLE Home Quantum Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  QLE Home  >  Th. List  >  ledior Unicode version
Theorem ledior 177
Description: Half of distributive law.
Assertion
Ref Expression
ledior ((b ^ c) v a) =< ((b v a) ^ (c v a))
Proof of Theorem ledior
StepHypRef Expression
1 ledio 176 . 2 (a v (b ^ c)) =< ((a v b) ^ (a v c))
2 ax-a2 31 . 2 ((b ^ c) v a) = (a v (b ^ c))
3 ax-a2 31 . . 3 (b v a) = (a v b)
4 ax-a2 31 . . 3 (c v a) = (a v c)
53, 42an 79 . 2 ((b v a) ^ (c v a)) = ((a v b) ^ (a v c))
61, 2, 5le3tr1 140 1 ((b ^ c) v a) =< ((b v a) ^ (c v a))
Colors of variables: term
Syntax hints:   =< wle 2   v wo 6   ^ wa 7
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-le1 130  df-le2 131
This theorem is referenced by:  oadistc0  1021
  Copyright terms: Public domain W3C validator