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Theorem equtr2OLD 1958
Description: Obsolete proof of equtr2 1956 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 1951 . . 3 (𝑧 = 𝑦 → (𝑥 = 𝑧𝑥 = 𝑦))
21equcoms 1949 . 2 (𝑦 = 𝑧 → (𝑥 = 𝑧𝑥 = 𝑦))
32impcom 446 1 ((𝑥 = 𝑧𝑦 = 𝑧) → 𝑥 = 𝑦)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 384
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1719  ax-4 1734  ax-5 1841  ax-6 1890  ax-7 1937
This theorem depends on definitions:  df-bi 197  df-an 386  df-ex 1702
This theorem is referenced by: (None)
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