QLE Home Quantum Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  QLE Home  >  Th. List  >  u3lemle1 Unicode version
Theorem u3lemle1 712
Description: L.e. to Kalmbach implication.
Hypothesis
Ref Expression
ulemle1.1 a =< b
Assertion
Ref Expression
u3lemle1 (a ->3 b) = 1
Proof of Theorem u3lemle1
StepHypRef Expression
1 ulemle1.1 . . . 4 a =< b
21lecom 180 . . 3 a C b
32u3lemc4 703 . 2 (a ->3 b) = (a' v b)
41sklem 230 . 2 (a' v b) = 1
53, 4ax-r2 36 1 (a ->3 b) = 1
Colors of variables: term
Syntax hints:   = wb 1   =< wle 2  'wn 4   v wo 6  1wt 8   ->3 wi3 14
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  ax-r3 439
This theorem depends on definitions:  df-b 39  df-a 40  df-t 41  df-f 42  df-i3 46  df-le1 130  df-le2 131  df-c1 132  df-c2 133
This theorem is referenced by:  u3lem14mp  794
  Copyright terms: Public domain W3C validator