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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 3939 | . . 3 | |
2 | neeq1 2258 | . . 3 | |
3 | 1, 2 | mpbiri 166 | . 2 |
4 | 3 | neneqd 2266 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wceq 1284 wne 2245 c0 3251 csn 3398 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-in1 576 ax-in2 577 ax-io 662 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-10 1436 ax-11 1437 ax-i12 1438 ax-bndl 1439 ax-4 1440 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 ax-nul 3904 |
This theorem depends on definitions: df-bi 115 df-tru 1287 df-nf 1390 df-sb 1686 df-clab 2068 df-cleq 2074 df-clel 2077 df-nfc 2208 df-ne 2246 df-v 2603 df-dif 2975 df-nul 3252 df-sn 3404 |
This theorem is referenced by: (None) |
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