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Mirrors > Home > ILE Home > Th. List > 0inp0 | Unicode version |
Description: Something cannot be equal to both the null set and the power set of the null set. (Contributed by NM, 30-Sep-2003.) |
Ref | Expression |
---|---|
0inp0 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 0nep0 4089 | . . 3 | |
2 | neeq1 2321 | . . 3 | |
3 | 1, 2 | mpbiri 167 | . 2 |
4 | 3 | neneqd 2329 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wceq 1331 wne 2308 c0 3363 csn 3527 |
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 ax-nul 4054 |
This theorem depends on definitions: df-bi 116 df-tru 1334 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 df-sn 3533 |
This theorem is referenced by: (None) |
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