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Theorem equtr 2032
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 2027 . 2 (𝑦 = 𝑥 → (𝑦 = 𝑧𝑥 = 𝑧))
21equcoms 2031 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 1802  ax-4 1816  ax-5 1916  ax-6 1974  ax-7 2019
This theorem depends on definitions:  df-bi 210  df-an 400  df-ex 1787
This theorem is referenced by:  equtrr  2033  equequ1  2036  equvinva  2041  ax6e  2382  equvini  2454  axprlem3  5289
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