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Theorem vextru 2720
Description: Every setvar is a member of {𝑥 ∣ ⊤}, which is therefore "a" universal class. Once class extensionality dfcleq 2729 is available, we can say "the" universal class (see df-v 3447). This is sbtru 2070 expressed using class abstractions. (Contributed by BJ, 2-Sep-2023.)
Assertion
Ref Expression
vextru 𝑦 ∈ {𝑥 ∣ ⊤}

Proof of Theorem vextru
StepHypRef Expression
1 tru 1545 . 2
21vexw 2719 1 𝑦 ∈ {𝑥 ∣ ⊤}
Colors of variables: wff setvar class
Syntax hints:  wtru 1542  wcel 2106  {cab 2713
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797
This theorem depends on definitions:  df-bi 206  df-tru 1544  df-sb 2068  df-clab 2714
This theorem is referenced by:  elisset  2819  vex  3449  abv  3456  ab0orv  4338  bj-denoteslem  35337  bj-vjust  35526
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