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Mirrors > Home > ILE Home > Th. List > n0r | GIF version |
Description: An inhabited class is nonempty. See n0rf 3345 for more discussion. (Contributed by Jim Kingdon, 31-Jul-2018.) |
Ref | Expression |
---|---|
n0r | ⊢ (∃𝑥 𝑥 ∈ 𝐴 → 𝐴 ≠ ∅) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfcv 2258 | . 2 ⊢ Ⅎ𝑥𝐴 | |
2 | 1 | n0rf 3345 | 1 ⊢ (∃𝑥 𝑥 ∈ 𝐴 → 𝐴 ≠ ∅) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∃wex 1453 ∈ wcel 1465 ≠ wne 2285 ∅c0 3333 |
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 588 ax-in2 589 ax-io 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 |
This theorem depends on definitions: df-bi 116 df-tru 1319 df-fal 1322 df-nf 1422 df-sb 1721 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-ne 2286 df-v 2662 df-dif 3043 df-nul 3334 |
This theorem is referenced by: neq0r 3347 opnzi 4127 elqsn0 6466 fin0 6747 infn0 6767 fsumcllem 11136 setsfun0 11922 |
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