QLE Home Quantum Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  QLE Home  >  Th. List  >  or42 GIF version

Theorem or42 85
Description: Rearrange disjuncts. (Contributed by NM, 4-Mar-2006.)
Assertion
Ref Expression
or42 ((ab) ∪ (cd)) = ((ad) ∪ (bc))

Proof of Theorem or42
StepHypRef Expression
1 ax-a2 31 . . 3 (cd) = (dc)
21lor 70 . 2 ((ab) ∪ (cd)) = ((ab) ∪ (dc))
3 or4 84 . 2 ((ab) ∪ (dc)) = ((ad) ∪ (bc))
42, 3ax-r2 36 1 ((ab) ∪ (cd)) = ((ad) ∪ (bc))
Colors of variables: term
Syntax hints:   = wb 1  wo 6
This theorem was proved from axioms:  ax-a2 31  ax-a3 32  ax-r1 35  ax-r2 36  ax-r5 38
This theorem is referenced by:  wdcom  1105
  Copyright terms: Public domain W3C validator