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Theorem equsb1v 2306
Description: Version of equsb1 2500 with a disjoint variable condition, which does not require ax-13 2391. (Contributed by BJ, 11-Sep-2019.)
Assertion
Ref Expression
equsb1v [𝑦 / 𝑥]𝑥 = 𝑦
Distinct variable group:   𝑥,𝑦

Proof of Theorem equsb1v
StepHypRef Expression
1 sb2v 2302 . 2 (∀𝑥(𝑥 = 𝑦𝑥 = 𝑦) → [𝑦 / 𝑥]𝑥 = 𝑦)
2 id 22 . 2 (𝑥 = 𝑦𝑥 = 𝑦)
31, 2mpg 1898 1 [𝑦 / 𝑥]𝑥 = 𝑦
Colors of variables: wff setvar class
Syntax hints:  wi 4  [wsb 2069
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-12 2222
This theorem depends on definitions:  df-bi 199  df-an 387  df-ex 1881  df-sb 2070
This theorem is referenced by:  sbiev  2345
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