Theorem vextru 2724

Description: Every setvar is a member of {𝑥 ∣ ⊤}, which is therefore "a" universal class. Once class extensionality dfcleq 2732 is available, we can say "the" universal class (see df-v 3433). This is sbtru 2078 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 1551	. 2 ⊢ ⊤
2	1	vexw 2723	1 ⊢ 𝑦 ∈ {𝑥 ∣ ⊤}

Syntax hints:  ⊤wtru 1548   ∈ wcel 2119  {cab 2717

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 208  df-tru 1550  df-sb 2074  df-clab 2718

This theorem is referenced by:  issettru  2817  vex  3435  abv  3443  vn0  4273  ab0orv  4311  bj-denoteslem  37224  bj-vjust  37408