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Theorem bj-vexwvt 32840
Description: Closed form of bj-vexwv 32841 and version of bj-vexwt 32838 with a dv condition, which does not require ax-13 2245. (Contributed by BJ, 13-Jun-2019.) (Proof modification is discouraged.)
Assertion
Ref Expression
bj-vexwvt (∀𝑥𝜑𝑦 ∈ {𝑥𝜑})
Distinct variable group:   𝑥,𝑦
Allowed substitution hints:   𝜑(𝑥,𝑦)

Proof of Theorem bj-vexwvt
StepHypRef Expression
1 bj-stdpc4v 32738 . 2 (∀𝑥𝜑 → [𝑦 / 𝑥]𝜑)
2 df-clab 2608 . 2 (𝑦 ∈ {𝑥𝜑} ↔ [𝑦 / 𝑥]𝜑)
31, 2sylibr 224 1 (∀𝑥𝜑𝑦 ∈ {𝑥𝜑})
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1480  [wsb 1879  wcel 1989  {cab 2607
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  df-clab 2608
This theorem is referenced by:  bj-vexwv  32841  bj-issetwt  32843  bj-abv  32885
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