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Theorem equsb1vOLD 2111
 Description: Obsolete version of equsb1v 2110 as of 22-Jul-2023. Version of equsb1 2512 with a disjoint variable condition, which neither requires ax-12 2176 nor ax-13 2382. (Contributed by BJ, 11-Sep-2019.) Remove dependencies on axioms. (Revised by Wolf Lammen, 30-May-2023.) (Proof shortened by Steven Nguyen, 19-Jun-2023.) Revise df-sb 2070. (Revised by Steven Nguyen, 11-Jul-2023.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
equsb1vOLD [𝑦 / 𝑥]𝑥 = 𝑦
Distinct variable group:   𝑥,𝑦

Proof of Theorem equsb1vOLD
StepHypRef Expression
1 sb2vOLD 2095 . 2 (∀𝑥(𝑥 = 𝑦𝑥 = 𝑦) → [𝑦 / 𝑥]𝑥 = 𝑦)
2 id 22 . 2 (𝑥 = 𝑦𝑥 = 𝑦)
31, 2mpg 1799 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 1797  ax-4 1811  ax-5 1911  ax-6 1970  ax-7 2015 This theorem depends on definitions:  df-bi 210  df-an 400  df-ex 1782  df-sb 2070 This theorem is referenced by: (None)
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