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Theorem sbeqal2i 41556
Description: If 𝑥 = 𝑦 implies 𝑥 = 𝑧, then we can infer 𝑧 = 𝑦. (Contributed by Andrew Salmon, 3-Jun-2011.)
Hypothesis
Ref Expression
sbeqal1i.1 (𝑥 = 𝑦𝑥 = 𝑧)
Assertion
Ref Expression
sbeqal2i 𝑧 = 𝑦
Distinct variable group:   𝑥,𝑧

Proof of Theorem sbeqal2i
StepHypRef Expression
1 sbeqal1i.1 . . 3 (𝑥 = 𝑦𝑥 = 𝑧)
21sbeqal1i 41555 . 2 𝑦 = 𝑧
32eqcomi 2747 1 𝑧 = 𝑦
Colors of variables: wff setvar class
Syntax hints:
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 1917  ax-6 1975  ax-7 2020  ax-9 2124  ax-10 2145  ax-12 2179  ax-13 2372  ax-ext 2710
This theorem depends on definitions:  df-bi 210  df-an 400  df-or 847  df-ex 1787  df-nf 1791  df-sb 2075  df-cleq 2730
This theorem is referenced by: (None)
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