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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 2730 is available, we can say "the" universal class (see df-v 3482). This is sbtru 2067 expressed using class abstractions. (Contributed by BJ, 2-Sep-2023.) |
| Ref | Expression |
|---|---|
| vextru | ⊢ 𝑦 ∈ {𝑥 ∣ ⊤} |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | tru 1544 | . 2 ⊢ ⊤ | |
| 2 | 1 | vexw 2720 | 1 ⊢ 𝑦 ∈ {𝑥 ∣ ⊤} |
| Colors of variables: wff setvar class |
| Syntax hints: ⊤wtru 1541 ∈ wcel 2108 {cab 2714 |
| This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1795 |
| This theorem depends on definitions: df-bi 207 df-tru 1543 df-sb 2065 df-clab 2715 |
| This theorem is referenced by: issettru 2819 vex 3484 abv 3492 ab0orv 4383 bj-denoteslem 36872 bj-vjust 37056 |
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