![]() |
Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > MPE Home > Th. List > vextru | Structured version Visualization version GIF version |
Description: Every setvar is a member of {𝑥 ∣ ⊤}, which is therefore "a" universal class. Once class extensionality dfcleq 2726 is available, we can say "the" universal class (see df-v 3449). This is sbtru 2071 expressed using class abstractions. (Contributed by BJ, 2-Sep-2023.) |
Ref | Expression |
---|---|
vextru | ⊢ 𝑦 ∈ {𝑥 ∣ ⊤} |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | tru 1546 | . 2 ⊢ ⊤ | |
2 | 1 | vexw 2716 | 1 ⊢ 𝑦 ∈ {𝑥 ∣ ⊤} |
Colors of variables: wff setvar class |
Syntax hints: ⊤wtru 1543 ∈ wcel 2107 {cab 2710 |
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 1545 df-sb 2069 df-clab 2711 |
This theorem is referenced by: elisset 2816 vex 3451 abv 3458 ab0orv 4342 bj-denoteslem 35390 bj-vjust 35576 |
Copyright terms: Public domain | W3C validator |