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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 2731 is available, we can say "the" universal class (see df-v 3399). This is sbtru 2076 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 2722 | 1 ⊢ 𝑦 ∈ {𝑥 ∣ ⊤} |
Colors of variables: wff setvar class |
Syntax hints: ⊤wtru 1543 ∈ wcel 2113 {cab 2716 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1802 |
This theorem depends on definitions: df-bi 210 df-tru 1545 df-sb 2074 df-clab 2717 |
This theorem is referenced by: elisset 2814 vex 3401 abv 3408 ab0orv 4264 bj-denoteslem 34675 bj-vjust 34838 |
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