Quantum Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  QLE Home  >  Th. List  >  i3li3 GIF version

Theorem i3li3 539
 Description: WQL (Weak Quantum Logic) rule.
Hypotheses
Ref Expression
i3li3.1 (a3 b) = 1
i3li3.2 (b3 a) = 1
Assertion
Ref Expression
i3li3 ((c3 a) →3 (c3 b)) = 1

Proof of Theorem i3li3
StepHypRef Expression
1 i3li3.1 . . . . . 6 (a3 b) = 1
21i3le 515 . . . . 5 ab
3 i3li3.2 . . . . . 6 (b3 a) = 1
43i3le 515 . . . . 5 ba
52, 4lebi 145 . . . 4 a = b
65li3 252 . . 3 (c3 a) = (c3 b)
76bile 142 . 2 (c3 a) ≤ (c3 b)
87lei3 246 1 ((c3 a) →3 (c3 b)) = 1
 Colors of variables: term Syntax hints:   = wb 1  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: (None)
 Copyright terms: Public domain W3C validator