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Theorem equtr 2016
Description: A transitive law for equality. (Contributed by NM, 23-Aug-1993.)
Assertion
Ref Expression
equtr (𝑥 = 𝑦 → (𝑦 = 𝑧𝑥 = 𝑧))

Proof of Theorem equtr
StepHypRef Expression
1 ax7 2011 . 2 (𝑦 = 𝑥 → (𝑦 = 𝑧𝑥 = 𝑧))
21equcoms 2015 1 (𝑥 = 𝑦 → (𝑦 = 𝑧𝑥 = 𝑧))
Colors of variables: wff setvar class
Syntax hints:  wi 4
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003
This theorem depends on definitions:  df-bi 206  df-an 396  df-ex 1774
This theorem is referenced by:  equtrr  2017  equequ1  2020  equvinva  2025  ax6e  2374  equvini  2446  axprlem3  5414
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