Theorem vextru 2715

Description: Every setvar is a member of {𝑥 ∣ ⊤}, which is therefore "a" universal class. Once class extensionality dfcleq 2724 is available, we can say "the" universal class (see df-v 3448). This is sbtru 2070 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 1545	. 2 ⊢ ⊤
2	1	vexw 2714	1 ⊢ 𝑦 ∈ {𝑥 ∣ ⊤}

Syntax hints:  ⊤wtru 1542   ∈ wcel 2106  {cab 2708

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797

This theorem depends on definitions:  df-bi 206  df-tru 1544  df-sb 2068  df-clab 2709

This theorem is referenced by:  elisset  2814  vex  3450  abv  3457  ab0orv  4343  bj-denoteslem  35413  bj-vjust  35599