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Theorem bj-vexwv 33183
Description: Version of bj-vexw 33181 with a dv condition, which does not require ax-13 2408. The degenerate instance of bj-vexw 33181 is a simple consequence of abid 2759 (which does not depend on ax-13 2408 either). (Contributed by BJ, 13-Jun-2019.) (Proof modification is discouraged.)
Hypothesis
Ref Expression
bj-vexwv.1 𝜑
Assertion
Ref Expression
bj-vexwv 𝑦 ∈ {𝑥𝜑}
Distinct variable group:   𝑥,𝑦
Allowed substitution hints:   𝜑(𝑥,𝑦)

Proof of Theorem bj-vexwv
StepHypRef Expression
1 bj-vexwvt 33182 . 2 (∀𝑥𝜑𝑦 ∈ {𝑥𝜑})
2 bj-vexwv.1 . 2 𝜑
31, 2mpg 1872 1 𝑦 ∈ {𝑥𝜑}
Colors of variables: wff setvar class
Syntax hints:  wcel 2145  {cab 2757
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1870  ax-4 1885  ax-5 1991  ax-6 2057  ax-7 2093  ax-12 2203
This theorem depends on definitions:  df-bi 197  df-an 383  df-ex 1853  df-sb 2050  df-clab 2758
This theorem is referenced by:  bj-denotes  33184  bj-rexvwv  33192  bj-rababwv  33193  bj-df-v  33344
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