Theorem vextru 2747

Description: Every setvar is a member of {𝑥 ∣ ⊤}, which is therefore "a" universal class. Once class extensionality dfcleq 2755 is available, we can say "the" universal class (see df-v 3456). This is sbtru 2096 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 1564	. 2 ⊢ ⊤
2	1	vexw 2746	1 ⊢ 𝑦 ∈ {𝑥 ∣ ⊤}

Syntax hints:  ⊤wtru 1561   ∈ wcel 2142  {cab 2740

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1815

This theorem depends on definitions:  df-bi 209  df-an 400  df-tru 1563  df-sb 2091  df-clab 2741

This theorem is referenced by:  issettru  2840  vex  3458  abv  3466  vn0  4297  ab0orv  4336  bj-denoteslem  37356  bj-vjust  37540