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

Step	Hyp	Ref	Expression
1		tru 1546	. 2 ⊢ ⊤
2	1	vexw 2722	1 ⊢ 𝑦 ∈ {𝑥 ∣ ⊤}

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