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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 2729 is available, we can say "the" universal class (see df-v 3447). This is sbtru 2070 expressed using class abstractions. (Contributed by BJ, 2-Sep-2023.) |
Ref | Expression |
---|---|
vextru | ⊢ 𝑦 ∈ {𝑥 ∣ ⊤} |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | tru 1545 | . 2 ⊢ ⊤ | |
2 | 1 | vexw 2719 | 1 ⊢ 𝑦 ∈ {𝑥 ∣ ⊤} |
Colors of variables: wff setvar class |
Syntax hints: ⊤wtru 1542 ∈ wcel 2106 {cab 2713 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1797 |
This theorem depends on definitions: df-bi 206 df-tru 1544 df-sb 2068 df-clab 2714 |
This theorem is referenced by: elisset 2819 vex 3449 abv 3456 ab0orv 4338 bj-denoteslem 35337 bj-vjust 35526 |
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