Quantum Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  QLE Home  >  Th. List  >  u1lem7 GIF version

Theorem u1lem7 772
 Description: Lemma for unified implication study. (Contributed by NM, 24-Dec-1997.)
Assertion
Ref Expression
u1lem7 (a1 (a1 b)) = 1

Proof of Theorem u1lem7
StepHypRef Expression
1 df-i1 44 . 2 (a1 (a1 b)) = (a ∪ (a ∩ (a1 b)))
2 ax-a1 30 . . . . . 6 a = a
32ran 78 . . . . 5 (a ∩ (a1 b)) = (a ∩ (a1 b))
4 ancom 74 . . . . . 6 (a ∩ (a1 b)) = ((a1 b) ∩ a )
5 u1lemana 605 . . . . . 6 ((a1 b) ∩ a ) = a
64, 5ax-r2 36 . . . . 5 (a ∩ (a1 b)) = a
73, 6ax-r2 36 . . . 4 (a ∩ (a1 b)) = a
87lor 70 . . 3 (a ∪ (a ∩ (a1 b))) = (aa )
9 df-t 41 . . . 4 1 = (aa )
109ax-r1 35 . . 3 (aa ) = 1
118, 10ax-r2 36 . 2 (a ∪ (a ∩ (a1 b))) = 1
121, 11ax-r2 36 1 (a1 (a1 b)) = 1
 Colors of variables: term Syntax hints:   = wb 1  ⊥ wn 4   ∪ wo 6   ∩ wa 7  1wt 8   →1 wi1 12 This theorem was proved from axioms:  ax-a1 30  ax-a2 31  ax-a5 34  ax-r1 35  ax-r2 36  ax-r4 37  ax-r5 38 This theorem depends on definitions:  df-a 40  df-t 41  df-i1 44 This theorem is referenced by: (None)
 Copyright terms: Public domain W3C validator