QLE Home Quantum Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  QLE Home  >  Th. List  >  lbi Unicode version
Theorem lbi 97
Description: Introduce biconditional to the left.
Hypothesis
Ref Expression
lbi.1 a = b
Assertion
Ref Expression
lbi (c == a) = (c == b)
Proof of Theorem lbi
StepHypRef Expression
1 lbi.1 . . . 4 a = b
21lan 77 . . 3 (c ^ a) = (c ^ b)
31ax-r4 37 . . . 4 a' = b'
43lan 77 . . 3 (c' ^ a') = (c' ^ b')
52, 42or 72 . 2 ((c ^ a) v (c' ^ a')) = ((c ^ b) v (c' ^ b'))
6 dfb 94 . 2 (c == a) = ((c ^ a) v (c' ^ a'))
7 dfb 94 . 2 (c == b) = ((c ^ b) v (c' ^ b'))
85, 6, 73tr1 63 1 (c == a) = (c == b)
Colors of variables: term
Syntax hints:   = wb 1  'wn 4   == tb 5   v wo 6   ^ wa 7
This theorem was proved from axioms:  ax-a1 30  ax-a2 31  ax-r1 35  ax-r2 36  ax-r4 37  ax-r5 38
This theorem depends on definitions:  df-b 39  df-a 40
This theorem is referenced by:  rbi  98  2bi  99  wcon3  209  wwoml2  212  nom55  336
  Copyright terms: Public domain W3C validator