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Mirrors > Home > ILE Home > Th. List > pw1ne0 | GIF version |
Description: The power set of 1o is not zero. (Contributed by Jim Kingdon, 30-Jul-2024.) |
Ref | Expression |
---|---|
pw1ne0 | ⊢ 𝒫 1o ≠ ∅ |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 0elpw 4189 | . 2 ⊢ ∅ ∈ 𝒫 1o | |
2 | 1 | ne0ii 3452 | 1 ⊢ 𝒫 1o ≠ ∅ |
Colors of variables: wff set class |
Syntax hints: ≠ wne 2360 ∅c0 3442 𝒫 cpw 3597 1oc1o 6449 |
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-in1 615 ax-in2 616 ax-io 710 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-10 1516 ax-11 1517 ax-i12 1518 ax-bndl 1520 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-ext 2171 ax-nul 4151 |
This theorem depends on definitions: df-bi 117 df-tru 1367 df-nf 1472 df-sb 1774 df-clab 2176 df-cleq 2182 df-clel 2185 df-nfc 2321 df-ne 2361 df-v 2758 df-dif 3151 df-in 3155 df-ss 3162 df-nul 3443 df-pw 3599 |
This theorem is referenced by: pw1nel3 7277 sucpw1nel3 7279 |
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