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Theorem equeuclr 2031
Description: Commuted version of equeucl 2032 (equality is left-Euclidean). (Contributed by BJ, 12-Apr-2021.)
Assertion
Ref Expression
equeuclr (𝑥 = 𝑧 → (𝑦 = 𝑧𝑦 = 𝑥))

Proof of Theorem equeuclr
StepHypRef Expression
1 equtrr 2030 . 2 (𝑧 = 𝑥 → (𝑦 = 𝑧𝑦 = 𝑥))
21equcoms 2028 1 (𝑥 = 𝑧 → (𝑦 = 𝑧𝑦 = 𝑥))
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 1797  ax-4 1811  ax-5 1912  ax-6 1971  ax-7 2016
This theorem depends on definitions:  df-bi 210  df-an 400  df-ex 1782
This theorem is referenced by:  equeucl  2032  equequ2  2034  ax13b  2040  aevlem0  2060  sbequivvOLD  2336  axc15  2446  equviniOLD  2480  sbequiOLD  2536  sbequiALT  2598  euequ  2684  sn-dtru  39262
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