Theorem vextru 2746

Description: Every setvar is a member of {𝑥 ∣ ⊤}, which is therefore "a" universal class. Once class extensionality dfcleq 2754 is available, we can say "the" universal class (see df-v 3453). This is sbtru 2104 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 2745	1 ⊢ 𝑦 ∈ {𝑥 ∣ ⊤}

This proof depends on syntax axioms:  ⊤wtru 1571   ∈ wcel 2145  {cab 2739

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828

This proof depends on definitions:  df-bi 210  df-tru 1573  df-sb 2100  df-clab 2740

This theorem is used by:  issettru  2839  vex  3455  abv  3463  vn0  4291  vn0OLD  4292  ab0orv  4332  bj-denoteslem  37783  bj-vjust  37970