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Theorem wed 441
Description: Weak equivalential detachment (WBMP). (Contributed by NM, 10-Aug-1997.)
Hypotheses
Ref Expression
wed.1 a = b
wed.2 (ab) = (cd)
Assertion
Ref Expression
wed c = d

Proof of Theorem wed
StepHypRef Expression
1 wed.1 . . . 4 a = b
211bi 119 . . 3 1 = (ab)
3 wed.2 . . 3 (ab) = (cd)
42, 3ax-r2 36 . 2 1 = (cd)
54r3a 440 1 c = d
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-a5 34  ax-r1 35  ax-r2 36  ax-r4 37  ax-r5 38  ax-r3 439
This theorem depends on definitions:  df-b 39  df-a 40  df-t 41  df-f 42
This theorem is referenced by:  r3b  442  i3th4  546
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