QLE Home Quantum Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  QLE Home  >  Th. List  >  leoa Unicode version
Theorem leoa 123
Description: Relation between two methods of expressing "less than or equal to".
Hypothesis
Ref Expression
leoa.1 (a v c) = b
Assertion
Ref Expression
leoa (a ^ b) = a
Proof of Theorem leoa
StepHypRef Expression
1 leoa.1 . . . 4 (a v c) = b
21ax-r1 35 . . 3 b = (a v c)
32lan 77 . 2 (a ^ b) = (a ^ (a v c))
4 anabs 121 . 2 (a ^ (a v c)) = a
53, 4ax-r2 36 1 (a ^ b) = a
Colors of variables: term
Syntax hints:   = wb 1   v wo 6   ^ wa 7
This theorem was proved from axioms:  ax-a1 30  ax-a2 31  ax-a5 34  ax-r1 35  ax-r2 36  ax-r4 37  ax-r5 38
This theorem depends on definitions:  df-a 40
This theorem is referenced by:  df2le2  136  wlem3.1  210
  Copyright terms: Public domain W3C validator