![]() |
Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
|
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 2560 | . 2 ⊢ 𝑥 ∈ V | |
2 | 19.8a 1482 | . 2 ⊢ (𝑥 ∈ V → ∃𝑥 𝑥 ∈ V) | |
3 | 1, 2 | ax-mp 7 | 1 ⊢ ∃𝑥 𝑥 ∈ V |
Colors of variables: wff set class |
Syntax hints: ∃wex 1381 ∈ wcel 1393 Vcvv 2557 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-5 1336 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-ext 2022 |
This theorem depends on definitions: df-bi 110 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-v 2559 |
This theorem is referenced by: relrelss 4844 |
Copyright terms: Public domain | W3C validator |