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Mirrors > Home > ILE Home > Th. List > vn0m | GIF version |
Description: The universal class is inhabited. (Contributed by Jim Kingdon, 17-Dec-2018.) |
Ref | Expression |
---|---|
vn0m | ⊢ ∃𝑥 𝑥 ∈ V |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | vex 2684 | . 2 ⊢ 𝑥 ∈ V | |
2 | 19.8a 1569 | . 2 ⊢ (𝑥 ∈ V → ∃𝑥 𝑥 ∈ V) | |
3 | 1, 2 | ax-mp 5 | 1 ⊢ ∃𝑥 𝑥 ∈ V |
Colors of variables: wff set class |
Syntax hints: ∃wex 1468 ∈ wcel 1480 Vcvv 2681 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-5 1423 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-ext 2119 |
This theorem depends on definitions: df-bi 116 df-sb 1736 df-clab 2124 df-cleq 2130 df-clel 2133 df-v 2683 |
This theorem is referenced by: relrelss 5060 |
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