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Theorem 3eqtr2i 2108
Description: An inference from three chained equalities. (Contributed by NM, 3-Aug-2006.)
Hypotheses
Ref Expression
3eqtr2i.1 𝐴 = 𝐵
3eqtr2i.2 𝐶 = 𝐵
3eqtr2i.3 𝐶 = 𝐷
Assertion
Ref Expression
3eqtr2i 𝐴 = 𝐷

Proof of Theorem 3eqtr2i
StepHypRef Expression
1 3eqtr2i.1 . . 3 𝐴 = 𝐵
2 3eqtr2i.2 . . 3 𝐶 = 𝐵
31, 2eqtr4i 2105 . 2 𝐴 = 𝐶
4 3eqtr2i.3 . 2 𝐶 = 𝐷
53, 4eqtri 2102 1 𝐴 = 𝐷
Colors of variables: wff set class
Syntax hints:   = wceq 1285
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1377  ax-gen 1379  ax-4 1441  ax-17 1460  ax-ext 2064
This theorem depends on definitions:  df-bi 115  df-cleq 2075
This theorem is referenced by:  dfrab3  3247  iunid  3741  cnvcnv  4803  cocnvcnv2  4862  fmptap  5385  negdii  7459  halfpm6th  8318  numma  8601  numaddc  8605  6p5lem  8627  8p2e10  8637  binom2i  9680  flodddiv4  10478  6gcd4e2  10528
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