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Theorem 3eqtr4d 2395
Description: A deduction from three chained equalities. (Contributed by NM, 4-Aug-1995.) (Proof shortened by Andrew Salmon, 25-May-2011.)
Hypotheses
Ref Expression
3eqtr4d.1
3eqtr4d.2
3eqtr4d.3
Assertion
Ref Expression
3eqtr4d

Proof of Theorem 3eqtr4d
StepHypRef Expression
1 3eqtr4d.2 . 2
2 3eqtr4d.3 . . 3
3 3eqtr4d.1 . . 3
42, 3eqtr4d 2388 . 2
51, 4eqtr4d 2388 1
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:  addcdir  6251
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