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Theorem equeuclr 2120
Description: Commuted version of equeucl 2121 (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 2119 . 2 (𝑧 = 𝑥 → (𝑦 = 𝑧𝑦 = 𝑥))
21equcoms 2117 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 1890  ax-4 1904  ax-5 2005  ax-6 2070  ax-7 2105
This theorem depends on definitions:  df-bi 198  df-an 385  df-ex 1875
This theorem is referenced by:  equeucl  2121  equequ2  2123  ax13b  2132  aevlem0  2147  equvini  2436  sbequi  2466  wl-ax8clv2  33828
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