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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 7630 | . 2 ⊢ 0 ∈ ℂ | |
2 | 1 | elexi 2653 | 1 ⊢ 0 ∈ V |
Colors of variables: wff set class |
Syntax hints: ∈ wcel 1448 Vcvv 2641 ℂcc 7498 0cc0 7500 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-5 1391 ax-gen 1393 ax-ie1 1437 ax-ie2 1438 ax-8 1450 ax-4 1455 ax-17 1474 ax-i9 1478 ax-ial 1482 ax-ext 2082 ax-1cn 7588 ax-icn 7590 ax-addcl 7591 ax-mulcl 7593 ax-i2m1 7600 |
This theorem depends on definitions: df-bi 116 df-sb 1704 df-clab 2087 df-cleq 2093 df-clel 2096 df-v 2643 |
This theorem is referenced by: elnn0 8831 nn0ex 8835 un0mulcl 8863 nn0ssz 8924 nn0ind-raph 9020 ser0f 10129 fser0const 10130 facnn 10314 fac0 10315 prhash2ex 10396 iserge0 10951 sum0 10996 isumz 10997 fisumss 11000 bezoutlemmain 11479 lcmval 11537 isomninnlem 12809 |
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