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Theorem 3eqtr2d 2078
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
3eqtr2d (𝜑𝐴 = 𝐷)

Proof of Theorem 3eqtr2d
StepHypRef Expression
1 3eqtr2d.1 . . 3 (𝜑𝐴 = 𝐵)
2 3eqtr2d.2 . . 3 (𝜑𝐶 = 𝐵)
31, 2eqtr4d 2075 . 2 (𝜑𝐴 = 𝐶)
4 3eqtr2d.3 . 2 (𝜑𝐶 = 𝐷)
53, 4eqtrd 2072 1 (𝜑𝐴 = 𝐷)
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:  fmptapd  5354  rdgisucinc  5972  mulidnq  6485  ltrnqg  6516  recexprlem1ssl  6729  recexprlem1ssu  6730  ltmprr  6738  mulcmpblnrlemg  6823  caucvgsrlemoffcau  6880  negsub  7257  neg2sub  7269  divmuleqap  7691  divneg2ap  7710  qapne  8572  binom2  9336  crim  9432  remullem  9445
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