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Theorem vexwt 2807
Description: A standard theorem of predicate calculus (stdpc4 2074) expressed using class abstractions. Closed form of vexw 2808. (Contributed by BJ, 14-Jun-2019.)
Assertion
Ref Expression
vexwt (∀𝑥𝜑𝑦 ∈ {𝑥𝜑})

Proof of Theorem vexwt
StepHypRef Expression
1 stdpc4 2074 . 2 (∀𝑥𝜑 → [𝑦 / 𝑥]𝜑)
2 df-clab 2803 . 2 (𝑦 ∈ {𝑥𝜑} ↔ [𝑦 / 𝑥]𝜑)
31, 2sylibr 237 1 (∀𝑥𝜑𝑦 ∈ {𝑥𝜑})
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1536  [wsb 2070  wcel 2115  {cab 2802
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 1912
This theorem depends on definitions:  df-bi 210  df-sb 2071  df-clab 2803
This theorem is referenced by:  bj-issetwt  34257  bj-abv  34291
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