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Theorem bj-equsb1v 32746
Description: Version of equsb1 2367 with a dv condition, which does not require ax-13 2245. (Contributed by BJ, 11-Sep-2019.) (Proof modification is discouraged.)
Assertion
Ref Expression
bj-equsb1v [𝑦 / 𝑥]𝑥 = 𝑦
Distinct variable group:   𝑥,𝑦

Proof of Theorem bj-equsb1v
StepHypRef Expression
1 bj-sb2v 32737 . 2 (∀𝑥(𝑥 = 𝑦𝑥 = 𝑦) → [𝑦 / 𝑥]𝑥 = 𝑦)
2 id 22 . 2 (𝑥 = 𝑦𝑥 = 𝑦)
31, 2mpg 1723 1 [𝑦 / 𝑥]𝑥 = 𝑦
Colors of variables: wff setvar class
Syntax hints:  wi 4  [wsb 1879
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1721  ax-4 1736  ax-5 1838  ax-6 1887  ax-7 1934  ax-12 2046
This theorem depends on definitions:  df-bi 197  df-an 386  df-ex 1704  df-sb 1880
This theorem is referenced by: (None)
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