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Theorem sbeqal1i 39440
 Description: Suppose you know 𝑥 = 𝑦 implies 𝑥 = 𝑧, assuming 𝑥 and 𝑧 are distinct. Then, 𝑦 = 𝑧. (Contributed by Andrew Salmon, 3-Jun-2011.)
Hypothesis
Ref Expression
sbeqal1i.1 (𝑥 = 𝑦𝑥 = 𝑧)
Assertion
Ref Expression
sbeqal1i 𝑦 = 𝑧
Distinct variable group:   𝑥,𝑧

Proof of Theorem sbeqal1i
StepHypRef Expression
1 sbeqal1 39439 . 2 (∀𝑥(𝑥 = 𝑦𝑥 = 𝑧) → 𝑦 = 𝑧)
2 sbeqal1i.1 . 2 (𝑥 = 𝑦𝑥 = 𝑧)
31, 2mpg 1898 1 𝑦 = 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 1896  ax-4 1910  ax-5 2011  ax-6 2077  ax-7 2114  ax-10 2194  ax-12 2222  ax-13 2391 This theorem depends on definitions:  df-bi 199  df-an 387  df-or 881  df-ex 1881  df-nf 1885  df-sb 2070 This theorem is referenced by:  sbeqal2i  39441
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