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Theorem bj-vexwvt 33182
Description: Closed form of bj-vexwv 33183 and version of bj-vexwt 33180 with a dv condition, which does not require ax-13 2422. (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 33089 . 2 (∀𝑥𝜑 → [𝑦 / 𝑥]𝜑)
2 df-clab 2804 . 2 (𝑦 ∈ {𝑥𝜑} ↔ [𝑦 / 𝑥]𝜑)
31, 2sylibr 225 1 (∀𝑥𝜑𝑦 ∈ {𝑥𝜑})
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1635  [wsb 2061  wcel 2157  {cab 2803
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1877  ax-4 1894  ax-5 2001  ax-6 2069  ax-7 2105  ax-12 2215
This theorem depends on definitions:  df-bi 198  df-an 385  df-ex 1860  df-sb 2062  df-clab 2804
This theorem is referenced by:  bj-vexwv  33183  bj-issetwt  33186  bj-abv  33228
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