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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 7905 | . 2 ⊢ 0 ∈ ℂ | |
2 | 1 | elexi 2742 | 1 ⊢ 0 ∈ V |
Colors of variables: wff set class |
Syntax hints: ∈ wcel 2141 Vcvv 2730 ℂcc 7765 0cc0 7767 |
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 1440 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-ext 2152 ax-1cn 7860 ax-icn 7862 ax-addcl 7863 ax-mulcl 7865 ax-i2m1 7872 |
This theorem depends on definitions: df-bi 116 df-sb 1756 df-clab 2157 df-cleq 2163 df-clel 2166 df-v 2732 |
This theorem is referenced by: elnn0 9130 nn0ex 9134 un0mulcl 9162 nn0ssz 9223 nn0ind-raph 9322 ser0f 10464 fser0const 10465 facnn 10654 fac0 10655 prhash2ex 10737 iserge0 11299 sum0 11344 isumz 11345 fisumss 11348 bezoutlemmain 11946 lcmval 12010 dvef 13447 2o01f 13994 iswomni0 14048 |
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