QLE Home Quantum Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  QLE Home  >  Th. List  >  u1lem7 Unicode version
Theorem u1lem7 772
Description: Lemma for unified implication study.
Assertion
Ref Expression
u1lem7 (a ->1 (a' ->1 b)) = 1
Proof of Theorem u1lem7
StepHypRef Expression
1 df-i1 44 . 2 (a ->1 (a' ->1 b)) = (a' v (a ^ (a' ->1 b)))
2 ax-a1 30 . . . . . 6 a = a''
32ran 78 . . . . 5 (a ^ (a' ->1 b)) = (a'' ^ (a' ->1 b))
4 ancom 74 . . . . . 6 (a'' ^ (a' ->1 b)) = ((a' ->1 b) ^ a'')
5 u1lemana 605 . . . . . 6 ((a' ->1 b) ^ a'') = a''
64, 5ax-r2 36 . . . . 5 (a'' ^ (a' ->1 b)) = a''
73, 6ax-r2 36 . . . 4 (a ^ (a' ->1 b)) = a''
87lor 70 . . 3 (a' v (a ^ (a' ->1 b))) = (a' v a'')
9 df-t 41 . . . 4 1 = (a' v a'')
109ax-r1 35 . . 3 (a' v a'') = 1
118, 10ax-r2 36 . 2 (a' v (a ^ (a' ->1 b))) = 1
121, 11ax-r2 36 1 (a ->1 (a' ->1 b)) = 1
Colors of variables: term
Syntax hints:   = wb 1  'wn 4   v 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