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Theorem w3tr2 375
 Description: Transitive inference useful for eliminating definitions.
Hypotheses
Ref Expression
w3tr2.1 (ab) = 1
w3tr2.2 (ac) = 1
w3tr2.3 (bd) = 1
Assertion
Ref Expression
w3tr2 (cd) = 1

Proof of Theorem w3tr2
StepHypRef Expression
1 w3tr2.1 . 2 (ab) = 1
2 w3tr2.2 . . 3 (ac) = 1
32wr1 197 . 2 (ca) = 1
4 w3tr2.3 . . 3 (bd) = 1
54wr1 197 . 2 (db) = 1
61, 3, 5w3tr1 374 1 (cd) = 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
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