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Theorem equtrr 2033
Description: A transitive law for equality. Lemma L17 in [Megill] p. 446 (p. 14 of the preprint). (Contributed by NM, 23-Aug-1993.)
Assertion
Ref Expression
equtrr (𝑥 = 𝑦 → (𝑧 = 𝑥𝑧 = 𝑦))

Proof of Theorem equtrr
StepHypRef Expression
1 equtr 2032 . 2 (𝑧 = 𝑥 → (𝑥 = 𝑦𝑧 = 𝑦))
21com12 32 1 (𝑥 = 𝑦 → (𝑧 = 𝑥𝑧 = 𝑦))
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:  equeuclr  2034  equequ2  2037  ax12v2  2180  2ax6elem  2469  axprlem3  5289  wl-spae  35292  ax12eq  36567  sn-axprlem3  39761  ax6e2eq  41699  ax6e2eqVD  42049
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