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Theorem wwbmp 205
Description: Weak weak equivalential detachment (WBMP).
Hypotheses
Ref Expression
wwbmp.1 a = 1
wwbmp.2 (a == b) = 1
Assertion
Ref Expression
wwbmp b = 1
Proof of Theorem wwbmp
StepHypRef Expression
1 wwbmp.1 . . . . 5 a = 1
21rbi 98 . . . 4 (a == b) = (1 == b)
32ax-r1 35 . . 3 (1 == b) = (a == b)
4 wwbmp.2 . . 3 (a == b) = 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
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