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Theorem 3eqtr2rd 2095
 Description: A deduction from three chained equalities. (Contributed by NM, 4-Aug-2006.)
Hypotheses
Ref Expression
3eqtr2d.1 (𝜑𝐴 = 𝐵)
3eqtr2d.2 (𝜑𝐶 = 𝐵)
3eqtr2d.3 (𝜑𝐶 = 𝐷)
Assertion
Ref Expression
3eqtr2rd (𝜑𝐷 = 𝐴)

Proof of Theorem 3eqtr2rd
StepHypRef Expression
1 3eqtr2d.1 . . 3 (𝜑𝐴 = 𝐵)
2 3eqtr2d.2 . . 3 (𝜑𝐶 = 𝐵)
31, 2eqtr4d 2091 . 2 (𝜑𝐴 = 𝐶)
4 3eqtr2d.3 . 2 (𝜑𝐶 = 𝐷)
53, 4eqtr2d 2089 1 (𝜑𝐷 = 𝐴)
 Colors of variables: wff set class Syntax hints:   → wi 4   = wceq 1259 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-5 1352  ax-gen 1354  ax-4 1416  ax-17 1435  ax-ext 2038 This theorem depends on definitions:  df-bi 114  df-cleq 2049 This theorem is referenced by:  prarloclemlo  6650  recexgt0sr  6916  xp1d2m1eqxm1d2  8234  qnegmod  9319  modqeqmodmin  9344  faclbnd2  9610  cjmulval  9716
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