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Theorem w3tr1 374
Description: Transitive inference useful for introducing definitions. (Contributed by NM, 13-Oct-1997.)
Hypotheses
Ref Expression
w3tr1.1 (ab) = 1
w3tr1.2 (ca) = 1
w3tr1.3 (db) = 1
Assertion
Ref Expression
w3tr1 (cd) = 1

Proof of Theorem w3tr1
StepHypRef Expression
1 w3tr1.2 . 2 (ca) = 1
2 w3tr1.1 . . 3 (ab) = 1
3 w3tr1.3 . . . 4 (db) = 1
43wr1 197 . . 3 (bd) = 1
52, 4wr2 371 . 2 (ad) = 1
61, 5wr2 371 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:  w3tr2  375  wcomlem  382  wbctr  410  wcomcom5  420  wfh1  423  wfh2  424  wdid0id5  1111  wdid0id1  1112  wdid0id2  1113  wdid0id3  1114
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