QLE Home Quantum Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  QLE Home  >  Th. List  >  w3tr2 Unicode version
Theorem w3tr2 375
Description: Transitive inference useful for eliminating definitions.
Hypotheses
Ref Expression
w3tr2.1 (a == b) = 1
w3tr2.2 (a == c) = 1
w3tr2.3 (b == d) = 1
Assertion
Ref Expression
w3tr2 (c == d) = 1
Proof of Theorem w3tr2
StepHypRef Expression
1 w3tr2.1 . 2 (a == b) = 1
2 w3tr2.2 . . 3 (a == c) = 1
32wr1 197 . 2 (c == a) = 1
4 w3tr2.3 . . 3 (b == d) = 1
54wr1 197 . 2 (d == b) = 1
61, 3, 5w3tr1 374 1 (c == d) = 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-a3 32  ax-a4 33  ax-a5 34  ax-r1 35  ax-r2 36  ax-r4 37  ax-r5 38  ax-wom 361
This theorem depends on definitions:  df-b 39  df-a 40  df-t 41  df-f 42  df-i1 44  df-i2 45  df-le1 130  df-le2 131
This theorem is referenced by:  wom4  380  wom5  381  wcomlem  382  wlecon  395  wletr  396  wcom3i  422  wfh3  425  wfh4  426  wlem14  430
  Copyright terms: Public domain W3C validator