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Theorem 3eqtr3d 2393
 Description: A deduction from three chained equalities. (Contributed by NM, 4-Aug-1995.) (Proof shortened by Andrew Salmon, 25-May-2011.)
Hypotheses
Ref Expression
3eqtr3d.1 (φA = B)
3eqtr3d.2 (φA = C)
3eqtr3d.3 (φB = D)
Assertion
Ref Expression
3eqtr3d (φC = D)

Proof of Theorem 3eqtr3d
StepHypRef Expression
1 3eqtr3d.1 . . 3 (φA = B)
2 3eqtr3d.2 . . 3 (φA = C)
31, 2eqtr3d 2387 . 2 (φB = C)
4 3eqtr3d.3 . 2 (φB = D)
53, 4eqtr3d 2387 1 (φC = D)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   = wceq 1642 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 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:  nnsucelr  4428  f1ocnvfv1  5476  enadj  6060  ncdisjun  6136
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