Theorem vextru 2754

Description: Every setvar is a member of {𝑥 ∣ ⊤}, which is therefore "a" universal class. Once class extensionality dfcleq 2762 is available, we can say "the" universal class (see df-v 3465). This is sbtru 2103 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 1571	. 2 ⊢ ⊤
2	1	vexw 2753	1 ⊢ 𝑦 ∈ {𝑥 ∣ ⊤}

Syntax hints:  ⊤wtru 1568   ∈ wcel 2149  {cab 2747

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1822

This theorem depends on definitions:  df-bi 210  df-an 401  df-tru 1570  df-sb 2098  df-clab 2748

This theorem is referenced by:  issettru  2847  vex  3467  abv  3475  vn0  4306  vn0OLD  4307  ab0orv  4346  bj-denoteslem  37395  bj-vjust  37579