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Mirrors > Home > ILE Home > Th. List > c0ex | GIF version |
Description: 0 is a set (common case). (Contributed by David A. Wheeler, 7-Jul-2016.) |
Ref | Expression |
---|---|
c0ex | ⊢ 0 ∈ V |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 0cn 7019 | . 2 ⊢ 0 ∈ ℂ | |
2 | 1 | elexi 2567 | 1 ⊢ 0 ∈ V |
Colors of variables: wff set class |
Syntax hints: ∈ wcel 1393 Vcvv 2557 ℂcc 6887 0cc0 6889 |
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 ax-1cn 6977 ax-icn 6979 ax-addcl 6980 ax-mulcl 6982 ax-i2m1 6989 |
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: elnn0 8183 nn0ex 8187 un0mulcl 8216 nn0ssz 8263 nn0ind-raph 8355 iser0f 9251 iserige0 9863 |
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