Theorem vextru 2722

Description: Every setvar is a member of {𝑥 ∣ ⊤}, which is therefore "a" universal class. Once class extensionality dfcleq 2731 is available, we can say "the" universal class (see df-v 3434). 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 1543	. 2 ⊢ ⊤
2	1	vexw 2721	1 ⊢ 𝑦 ∈ {𝑥 ∣ ⊤}

Syntax hints:  ⊤wtru 1540   ∈ wcel 2106  {cab 2715

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798

This theorem depends on definitions:  df-bi 206  df-tru 1542  df-sb 2068  df-clab 2716

This theorem is referenced by:  elisset  2820  vex  3436  abv  3443  ab0orv  4312  bj-denoteslem  35055  bj-vjust  35226