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

Theorem wwbmp 205
 Description: Weak weak equivalential detachment (WBMP).
Hypotheses
Ref Expression
wwbmp.1 a = 1
wwbmp.2 (ab) = 1
Assertion
Ref Expression
wwbmp b = 1

Proof of Theorem wwbmp
StepHypRef Expression
1 wwbmp.1 . . . . 5 a = 1
21rbi 98 . . . 4 (ab) = (1 ≡ b)
32ax-r1 35 . . 3 (1 ≡ b) = (ab)
4 wwbmp.2 . . 3 (ab) = 1
53, 4ax-r2 36 . 2 (1 ≡ b) = 1
65wr3 198 1 b = 1
 Colors of variables: term Syntax hints:   = wb 1   ≡ tb 5  1wt 8 This theorem was proved from axioms:  ax-a1 30  ax-a2 31  ax-a4 33  ax-a5 34  ax-r1 35  ax-r2 36  ax-r4 37  ax-r5 38 This theorem depends on definitions:  df-b 39  df-a 40  df-t 41  df-f 42 This theorem is referenced by:  wwbmpr  206  bina1  282  bina2  283  wr2  371  ska2  432  i3abs2  523  i3orcom  525  i3ancom  526  i3btr  528  wdid0id5  1109  wdid0id1  1110  wdid0id2  1111  wdid0id3  1112  wdid0id4  1113
 Copyright terms: Public domain W3C validator