Theorem vextru 2719

Description: Every setvar is a member of {𝑥 ∣ ⊤}, which is therefore "a" universal class. Once class extensionality dfcleq 2728 is available, we can say "the" universal class (see df-v 3480). This is sbtru 2065 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 1541	. 2 ⊢ ⊤
2	1	vexw 2718	1 ⊢ 𝑦 ∈ {𝑥 ∣ ⊤}

Syntax hints:  ⊤wtru 1538   ∈ wcel 2106  {cab 2712

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792

This theorem depends on definitions:  df-bi 207  df-tru 1540  df-sb 2063  df-clab 2713

This theorem is referenced by:  issettru  2817  vex  3482  abv  3490  ab0orv  4389  bj-denoteslem  36854  bj-vjust  37038