NFE Home New Foundations Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  NFE Home  >  Th. List  >  3eqtrrd Unicode version

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
3eqtrd.2
3eqtrd.3
Assertion
Ref Expression
3eqtrrd

Proof of Theorem 3eqtrrd
StepHypRef Expression
1 3eqtrd.1 . . 3
2 3eqtrd.2 . . 3
31, 2eqtrd 2385 . 2
4 3eqtrd.3 . 2
53, 4eqtr2d 2386 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: (None)
  Copyright terms: Public domain W3C validator