MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  equtr2OLD Structured version   Visualization version   GIF version

Theorem equtr2OLD 1943
Description: Obsolete proof of equtr2 1941 as of 11-Apr-2021. (Contributed by NM, 12-Aug-1993.) (Proof shortened by Andrew Salmon, 25-May-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
equtr2OLD ((𝑥 = 𝑧𝑦 = 𝑧) → 𝑥 = 𝑦)

Proof of Theorem equtr2OLD
StepHypRef Expression
1 equtrr 1936 . . 3 (𝑧 = 𝑦 → (𝑥 = 𝑧𝑥 = 𝑦))
21equcoms 1934 . 2 (𝑦 = 𝑧 → (𝑥 = 𝑧𝑥 = 𝑦))
32impcom 445 1 ((𝑥 = 𝑧𝑦 = 𝑧) → 𝑥 = 𝑦)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 383
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922
This theorem depends on definitions:  df-bi 196  df-an 385  df-ex 1696
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator