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Theorem vextru 2723
Description: Every setvar is a member of {𝑥 ∣ ⊤}, which is therefore "a" universal class. Once class extensionality dfcleq 2731 is available, we can say "the" universal class (see df-v 3399). This is sbtru 2076 expressed using class abstractions. (Contributed by BJ, 2-Sep-2023.)
Assertion
Ref Expression
vextru 𝑦 ∈ {𝑥 ∣ ⊤}

Proof of Theorem vextru
StepHypRef Expression
1 tru 1546 . 2
21vexw 2722 1 𝑦 ∈ {𝑥 ∣ ⊤}
Colors of variables: wff setvar class
Syntax hints:  wtru 1543  wcel 2113  {cab 2716
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1802
This theorem depends on definitions:  df-bi 210  df-tru 1545  df-sb 2074  df-clab 2717
This theorem is referenced by:  elisset  2814  vex  3401  abv  3408  ab0orv  4264  bj-denoteslem  34675  bj-vjust  34838
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