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Theorem 3eqtr3rd 2081
 Description: A deduction from three chained equalities. (Contributed by NM, 14-Jan-2006.)
Hypotheses
Ref Expression
3eqtr3d.1 (𝜑𝐴 = 𝐵)
3eqtr3d.2 (𝜑𝐴 = 𝐶)
3eqtr3d.3 (𝜑𝐵 = 𝐷)
Assertion
Ref Expression
3eqtr3rd (𝜑𝐷 = 𝐶)

Proof of Theorem 3eqtr3rd
StepHypRef Expression
1 3eqtr3d.3 . 2 (𝜑𝐵 = 𝐷)
2 3eqtr3d.1 . . 3 (𝜑𝐴 = 𝐵)
3 3eqtr3d.2 . . 3 (𝜑𝐴 = 𝐶)
42, 3eqtr3d 2074 . 2 (𝜑𝐵 = 𝐶)
51, 4eqtr3d 2074 1 (𝜑𝐷 = 𝐶)
 Colors of variables: wff set class Syntax hints:   → wi 4   = wceq 1243 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1336  ax-gen 1338  ax-4 1400  ax-17 1419  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-cleq 2033 This theorem is referenced by:  fcofo  5424  fcof1o  5429  nnaword  6084  pn0sr  6856  negeu  7202  add20  7469  2halves  8154  resqrexlemover  9608
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