QLE Home Quantum Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  QLE Home  >  Th. List  >  u3lemc2 GIF version

Theorem u3lemc2 688
Description: Commutation theorem for Kalmbach implication. (Contributed by NM, 14-Dec-1997.)
Hypotheses
Ref Expression
ulemc2.1 a C b
ulemc2.2 a C c
Assertion
Ref Expression
u3lemc2 a C (b3 c)

Proof of Theorem u3lemc2
StepHypRef Expression
1 ulemc2.1 . 2 a C b
2 ulemc2.2 . 2 a C c
31, 2com2i3 509 1 a C (b3 c)
Colors of variables: term
Syntax hints:   C wc 3  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:  u3lem2  746
  Copyright terms: Public domain W3C validator