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Theorem 3eqtr2i 2066
 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 2063 . 2 𝐴 = 𝐶
4 3eqtr2i.3 . 2 𝐶 = 𝐷
53, 4eqtri 2060 1 𝐴 = 𝐷
 Colors of variables: wff set class Syntax hints:   = wceq 1243 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1336  ax-gen 1338  ax-4 1400  ax-17 1419  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-cleq 2033 This theorem is referenced by:  dfrab3  3213  iunid  3712  cnvcnv  4773  cocnvcnv2  4832  fmptap  5353  negdii  7295  halfpm6th  8145  numma  8398  numaddc  8402  6p5lem  8416  binom2i  9360
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