Quantum Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  QLE Home  >  Th. List  >  u3lemnaa GIF version

Theorem u3lemnaa 642
 Description: Lemma for Kalmbach implication study.
Assertion
Ref Expression
u3lemnaa ((a3 b)a) = (ab )

Proof of Theorem u3lemnaa
StepHypRef Expression
1 anor2 89 . 2 ((a3 b)a) = ((a3 b) ∪ a )
2 anor1 88 . . . 4 (ab ) = (ab)
3 u3lemona 627 . . . . . 6 ((a3 b) ∪ a ) = (ab)
43ax-r4 37 . . . . 5 ((a3 b) ∪ a ) = (ab)
54ax-r1 35 . . . 4 (ab) = ((a3 b) ∪ a )
62, 5ax-r2 36 . . 3 (ab ) = ((a3 b) ∪ a )
76ax-r1 35 . 2 ((a3 b) ∪ a ) = (ab )
81, 7ax-r2 36 1 ((a3 b)a) = (ab )
 Colors of variables: term Syntax hints:   = wb 1  ⊥ wn 4   ∪ wo 6   ∩ wa 7   →3 wi3 14 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  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 This theorem is referenced by:  u3lem13a  789  u3lem13b  790
 Copyright terms: Public domain W3C validator