MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  vextru Structured version   Visualization version   GIF version

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
StepHypRef Expression
1 tru 1543 . 2
21vexw 2721 1 𝑦 ∈ {𝑥 ∣ ⊤}
Colors of variables: wff setvar class
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
  Copyright terms: Public domain W3C validator