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Mirrors > Home > ILE Home > Th. List > n0r | GIF version |
Description: An inhabited class is nonempty. See n0rf 3375 for more discussion. (Contributed by Jim Kingdon, 31-Jul-2018.) |
Ref | Expression |
---|---|
n0r | ⊢ (∃𝑥 𝑥 ∈ 𝐴 → 𝐴 ≠ ∅) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfcv 2281 | . 2 ⊢ Ⅎ𝑥𝐴 | |
2 | 1 | n0rf 3375 | 1 ⊢ (∃𝑥 𝑥 ∈ 𝐴 → 𝐴 ≠ ∅) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∃wex 1468 ∈ wcel 1480 ≠ wne 2308 ∅c0 3363 |
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-in1 603 ax-in2 604 ax-io 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 |
This theorem depends on definitions: df-bi 116 df-tru 1334 df-fal 1337 df-nf 1437 df-sb 1736 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-ne 2309 df-v 2688 df-dif 3073 df-nul 3364 |
This theorem is referenced by: neq0r 3377 opnzi 4157 elqsn0 6498 fin0 6779 infn0 6799 fsumcllem 11168 setsfun0 11995 |
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