QLE Home Quantum Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  QLE Home  >  Th. List  >  3vth8 GIF version

Theorem 3vth8 811
Description: A 3-variable theorem. (Contributed by NM, 18-Oct-1998.)
Assertion
Ref Expression
3vth8 (a2 (bc)) = (((a2 b) ∩ (c2 b)) ∪ ((a2 c) ∩ (b2 c)))

Proof of Theorem 3vth8
StepHypRef Expression
1 3vth7 810 . . 3 ((a2 b)2 (bc)) = (a2 (bc))
21ax-r1 35 . 2 (a2 (bc)) = ((a2 b)2 (bc))
3 3vth6 809 . 2 ((a2 b)2 (bc)) = (((a2 b) ∩ (c2 b)) ∪ ((a2 c) ∩ (b2 c)))
42, 3ax-r2 36 1 (a2 (bc)) = (((a2 b) ∩ (c2 b)) ∪ ((a2 c) ∩ (b2 c)))
Colors of variables: term
Syntax hints:   = wb 1   wn 4  wo 6  wa 7  2 wi2 13
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-i2 45  df-le1 130  df-le2 131  df-c1 132  df-c2 133
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator