Theorem vextru 2745

Description: Every setvar is a member of {𝑥 ∣ ⊤}, which is therefore "a" universal class. Once class extensionality dfcleq 2753 is available, we can say "the" universal class (see df-v 3452). 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 1573	. 2 ⊢ ⊤
2	1	vexw 2744	1 ⊢ 𝑦 ∈ {𝑥 ∣ ⊤}

This proof depends on syntax axioms:  ⊤wtru 1570   ∈ wcel 2144  {cab 2738

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1827

This proof depends on definitions:  df-bi 210  df-tru 1572  df-sb 2099  df-clab 2739

This theorem is used by:  issettru  2838  vex  3454  abv  3462  vn0  4290  vn0OLD  4291  ab0orv  4331  bj-denoteslem  37907  bj-vjust  38106