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Theorem equtr 1945
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 1940 . 2 (𝑦 = 𝑥 → (𝑦 = 𝑧𝑥 = 𝑧))
21equcoms 1944 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 1719  ax-4 1734  ax-5 1836  ax-6 1885  ax-7 1932
This theorem depends on definitions:  df-bi 197  df-an 386  df-ex 1702
This theorem is referenced by:  equtrr  1946  equequ1  1949  equviniva  1957  ax6e  2249  equvini  2345  sbequi  2374  axsep  4740  bj-axsep  32436
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