QLE Home Quantum Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  QLE Home  >  Th. List  >  i32an GIF version

Theorem i32an 537
Description: WQL (Weak Quantum Logic) rule. (Contributed by NM, 7-Nov-1997.)
Hypotheses
Ref Expression
i32an.1 (a3 b) = 1
i32an.2 (c3 d) = 1
Assertion
Ref Expression
i32an ((ac) →3 (bd)) = 1

Proof of Theorem i32an
StepHypRef Expression
1 i32an.1 . . 3 (a3 b) = 1
21i3ran 535 . 2 ((ac) →3 (bc)) = 1
3 i32an.2 . . 3 (c3 d) = 1
43i3lan 536 . 2 ((bc) →3 (bd)) = 1
52, 4binr2 518 1 ((ac) →3 (bd)) = 1
Colors of variables: term
Syntax hints:   = wb 1  wa 7  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