QLE Home Quantum Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  QLE Home  >  Th. List  >  u2lemnaa GIF version

Theorem u2lemnaa 641
Description: Lemma for Dishkant implication study. (Contributed by NM, 15-Dec-1997.)
Assertion
Ref Expression
u2lemnaa ((a2 b)a) = (ab )

Proof of Theorem u2lemnaa
StepHypRef Expression
1 anor2 89 . . 3 ((a2 b)a) = ((a2 b) ∪ a )
2 u2lemona 626 . . . 4 ((a2 b) ∪ a ) = (ab)
32ax-r4 37 . . 3 ((a2 b) ∪ a ) = (ab)
41, 3ax-r2 36 . 2 ((a2 b)a) = (ab)
5 anor1 88 . . 3 (ab ) = (ab)
65ax-r1 35 . 2 (ab) = (ab )
74, 6ax-r2 36 1 ((a2 b)a) = (ab )
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-a5 34  ax-r1 35  ax-r2 36  ax-r4 37  ax-r5 38
This theorem depends on definitions:  df-a 40  df-i2 45  df-le1 130  df-le2 131
This theorem is referenced by:  u2lem7  773
  Copyright terms: Public domain W3C validator