QLE Home Quantum Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  QLE Home  >  Th. List  >  u1lemnanb GIF version

Theorem u1lemnanb 655
Description: Lemma for Sasaki implication study. (Contributed by NM, 16-Dec-1997.)
Assertion
Ref Expression
u1lemnanb ((a1 b)b ) = (ab )

Proof of Theorem u1lemnanb
StepHypRef Expression
1 u1lemob 630 . . 3 ((a1 b) ∪ b) = (ab)
2 oran 87 . . 3 ((a1 b) ∪ b) = ((a1 b)b )
3 oran2 92 . . 3 (ab) = (ab )
41, 2, 33tr2 64 . 2 ((a1 b)b ) = (ab )
54con1 66 1 ((a1 b)b ) = (ab )
Colors of variables: term
Syntax hints:   = wb 1   wn 4  wo 6  wa 7  1 wi1 12
This theorem was proved from axioms:  ax-a1 30  ax-a2 31  ax-a3 32  ax-a5 34  ax-r1 35  ax-r2 36  ax-r4 37  ax-r5 38
This theorem depends on definitions:  df-a 40  df-i1 44  df-le1 130  df-le2 131
This theorem is referenced by:  u3lem14a  791
  Copyright terms: Public domain W3C validator