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Theorem 3eqtrd 2389
 Description: A deduction from three chained equalities. (Contributed by NM, 29-Oct-1995.)
Hypotheses
Ref Expression
3eqtrd.1 (φA = B)
3eqtrd.2 (φB = C)
3eqtrd.3 (φC = D)
Assertion
Ref Expression
3eqtrd (φA = D)

Proof of Theorem 3eqtrd
StepHypRef Expression
1 3eqtrd.1 . 2 (φA = B)
2 3eqtrd.2 . . 3 (φB = C)
3 3eqtrd.3 . . 3 (φC = D)
42, 3eqtrd 2385 . 2 (φB = D)
51, 4eqtrd 2385 1 (φA = 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:  tpeq123d  3814  diftpsn3  3849  vfinncsp  4554  fvun  5378  oveq123d  5543  fvmptd  5702
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