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Theorem eqtr2OLD 2762
Description: Obsolete version of eqtr2 as of 24-Oct-2024. (Contributed by NM, 20-May-2005.) (Proof shortened by Andrew Salmon, 25-May-2011.) (New usage is discouraged.) (Proof modification is discouraged.)
Assertion
Ref Expression
eqtr2OLD ((𝐴 = 𝐵𝐴 = 𝐶) → 𝐵 = 𝐶)

Proof of Theorem eqtr2OLD
StepHypRef Expression
1 eqcom 2744 . 2 (𝐴 = 𝐵𝐵 = 𝐴)
2 eqtr 2760 . 2 ((𝐵 = 𝐴𝐴 = 𝐶) → 𝐵 = 𝐶)
31, 2sylanb 584 1 ((𝐴 = 𝐵𝐴 = 𝐶) → 𝐵 = 𝐶)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 399   = wceq 1543
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1803  ax-4 1817  ax-5 1918  ax-6 1976  ax-7 2016  ax-9 2120  ax-ext 2708
This theorem depends on definitions:  df-bi 210  df-an 400  df-ex 1788  df-cleq 2729
This theorem is referenced by: (None)
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