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Theorem 3eqtrri 2378
 Description: An inference from three chained equalities. (Contributed by NM, 3-Aug-2006.) (Proof shortened by Andrew Salmon, 25-May-2011.)
Hypotheses
Ref Expression
3eqtri.1 A = B
3eqtri.2 B = C
3eqtri.3 C = D
Assertion
Ref Expression
3eqtrri D = A

Proof of Theorem 3eqtrri
StepHypRef Expression
1 3eqtri.1 . . 3 A = B
2 3eqtri.2 . . 3 B = C
31, 2eqtri 2373 . 2 A = C
4 3eqtri.3 . 2 C = D
53, 4eqtr2i 2374 1 D = A
 Colors of variables: wff setvar class Syntax hints:   = wceq 1642 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-11 1746  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-ex 1542  df-cleq 2346 This theorem is referenced by:  dfun4  3546  dfif5  3674  compldif  4069  opeq  4619  mucnc  6131  nnc3n3p2  6279
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