QLE Home Quantum Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  QLE Home  >  Th. List  >  u1lemn1b Unicode version
Theorem u1lemn1b 730
Description: This theorem continues the line of proofs such as u1lemnaa 640, ud1lem0b 256, u1lemnanb 655, etc. (Contributed by Josiah Burroughs 26-May-04.)
Assertion
Ref Expression
u1lemn1b (a ->1 b) = ((a ->1 b)' ->1 b)
Proof of Theorem u1lemn1b
StepHypRef Expression
1 ax-a1 30 . . 3 (a ->1 b) = (a ->1 b)''
2 u1lemnab 650 . . . 4 ((a ->1 b)' ^ b) = 0
32ax-r1 35 . . 3 0 = ((a ->1 b)' ^ b)
41, 32or 72 . 2 ((a ->1 b) v 0) = ((a ->1 b)'' v ((a ->1 b)' ^ b))
5 or0 102 . . 3 ((a ->1 b) v 0) = (a ->1 b)
65ax-r1 35 . 2 (a ->1 b) = ((a ->1 b) v 0)
7 df-i1 44 . 2 ((a ->1 b)' ->1 b) = ((a ->1 b)'' v ((a ->1 b)' ^ b))
84, 6, 73tr1 63 1 (a ->1 b) = ((a ->1 b)' ->1 b)
Colors of variables: term
Syntax hints:   = wb 1  'wn 4   v wo 6   ^ wa 7  0wf 9   ->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-t 41  df-f 42  df-i1 44
This theorem is referenced by:  u1lem3var1  731  lem4.6.5  1085
  Copyright terms: Public domain W3C validator