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Theorem 3eqtrrd 2390
Description: A deduction from three chained equalities. (Contributed by NM, 4-Aug-2006.) (Proof shortened by Andrew Salmon, 25-May-2011.)
Hypotheses
Ref Expression
3eqtrd.1 (φA = B)
3eqtrd.2 (φB = C)
3eqtrd.3 (φC = D)
Assertion
Ref Expression
3eqtrrd (φD = A)

Proof of Theorem 3eqtrrd
StepHypRef Expression
1 3eqtrd.1 . . 3 (φA = B)
2 3eqtrd.2 . . 3 (φB = C)
31, 2eqtrd 2385 . 2 (φA = C)
4 3eqtrd.3 . 2 (φC = D)
53, 4eqtr2d 2386 1 (φD = A)
Colors of variables: wff setvar class
Syntax hints:  wi 4   = 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: (None)
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