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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 7979 | . 2 ⊢ 0 ∈ ℂ | |
2 | 1 | elexi 2764 | 1 ⊢ 0 ∈ V |
Colors of variables: wff set class |
Syntax hints: ∈ wcel 2160 Vcvv 2752 ℂcc 7839 0cc0 7841 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-5 1458 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-ext 2171 ax-1cn 7934 ax-icn 7936 ax-addcl 7937 ax-mulcl 7939 ax-i2m1 7946 |
This theorem depends on definitions: df-bi 117 df-sb 1774 df-clab 2176 df-cleq 2182 df-clel 2185 df-v 2754 |
This theorem is referenced by: elnn0 9208 nn0ex 9212 un0mulcl 9240 nn0ssz 9301 nn0ind-raph 9400 ser0f 10546 fser0const 10547 facnn 10739 fac0 10740 prhash2ex 10821 iserge0 11383 sum0 11428 isumz 11429 fisumss 11432 bezoutlemmain 12031 lcmval 12095 dvef 14645 2o01f 15205 iswomni0 15258 |
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