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Theorem 3eqtr3g 2408
 Description: A chained equality inference, useful for converting from definitions. (Contributed by NM, 15-Nov-1994.)
Hypotheses
Ref Expression
3eqtr3g.1 (φA = B)
3eqtr3g.2 A = C
3eqtr3g.3 B = D
Assertion
Ref Expression
3eqtr3g (φC = D)

Proof of Theorem 3eqtr3g
StepHypRef Expression
1 3eqtr3g.2 . . 3 A = C
2 3eqtr3g.1 . . 3 (φA = B)
31, 2syl5eqr 2399 . 2 (φC = B)
4 3eqtr3g.3 . 2 B = D
53, 4syl6eq 2401 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:  csbnest1g  3188  nineq2  3235  compleqb  3543  adj11  3889  pw1eqadj  4332  tfindi  4496  opth  4602  xpid11  4926  cnveqb  5063  cores2  5091  fvunsn  5444  nchoicelem1  6289
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