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Mirrors > Home > ILE Home > Th. List > n0r | GIF version |
Description: An inhabited class is nonempty. See n0rf 3233 for more discussion. (Contributed by Jim Kingdon, 31-Jul-2018.) |
Ref | Expression |
---|---|
n0r | ⊢ (∃𝑥 𝑥 ∈ 𝐴 → 𝐴 ≠ ∅) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfcv 2178 | . 2 ⊢ Ⅎ𝑥𝐴 | |
2 | 1 | n0rf 3233 | 1 ⊢ (∃𝑥 𝑥 ∈ 𝐴 → 𝐴 ≠ ∅) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∃wex 1381 ∈ wcel 1393 ≠ wne 2204 ∅c0 3224 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-in1 544 ax-in2 545 ax-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 |
This theorem depends on definitions: df-bi 110 df-tru 1246 df-fal 1249 df-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-ne 2206 df-v 2559 df-dif 2920 df-nul 3225 |
This theorem is referenced by: neq0r 3235 opnzi 3972 elqsn0 6175 fin0 6342 |
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