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Theorem 3eqtr3ri 2382
Description: An inference from three chained equalities. (Contributed by NM, 15-Aug-2004.)
Hypotheses
Ref Expression
3eqtr3i.1 A = B
3eqtr3i.2 A = C
3eqtr3i.3 B = D
Assertion
Ref Expression
3eqtr3ri D = C

Proof of Theorem 3eqtr3ri
StepHypRef Expression
1 3eqtr3i.3 . 2 B = D
2 3eqtr3i.1 . . 3 A = B
3 3eqtr3i.2 . . 3 A = C
42, 3eqtr3i 2375 . 2 B = C
51, 4eqtr3i 2375 1 D = C
Colors of variables: wff setvar class
Syntax hints:   = 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:  indif2  3498  dfif5  3674  nchoicelem2  6290
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