Theorem vextru 2748

Description: Every setvar is a member of {𝑥 ∣ ⊤}, which is therefore "a" universal class. Once class extensionality dfcleq 2756 is available, we can say "the" universal class (see df-v 3457). This is sbtru 2101 expressed using class abstractions. (Contributed by BJ, 2-Sep-2023.)

Assertion

Ref	Expression
vextru	⊢ 𝑦 ∈ {𝑥 ∣ ⊤}

Proof of Theorem vextru

Step	Hyp	Ref	Expression
1		tru 1574	. 2 ⊢ ⊤
2	1	vexw 2747	1 ⊢ 𝑦 ∈ {𝑥 ∣ ⊤}

Syntax hints:  ⊤wtru 1571   ∈ wcel 2143  {cab 2741

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1825

This theorem depends on definitions:  df-bi 210  df-tru 1573  df-sb 2097  df-clab 2742

This theorem is referenced by:  issettru  2841  vex  3459  abv  3467  vn0  4298  vn0OLD  4299  ab0orv  4339  bj-denoteslem  37526  bj-vjust  37711