MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  eqtr3OLD Structured version   Visualization version   GIF version

Theorem eqtr3OLD 2764
Description: Obsolete version of eqtr3 2763 as of 24-Oct-2024. (Contributed by NM, 20-May-2005.) (New usage is discouraged.) (Proof modification is discouraged.)
Assertion
Ref Expression
eqtr3OLD ((𝐴 = 𝐶𝐵 = 𝐶) → 𝐴 = 𝐵)

Proof of Theorem eqtr3OLD
StepHypRef Expression
1 eqcom 2744 . 2 (𝐵 = 𝐶𝐶 = 𝐵)
2 eqtr 2760 . 2 ((𝐴 = 𝐶𝐶 = 𝐵) → 𝐴 = 𝐵)
31, 2sylan2b 597 1 ((𝐴 = 𝐶𝐵 = 𝐶) → 𝐴 = 𝐵)
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)
  Copyright terms: Public domain W3C validator