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Mirrors > Home > ILE Home > Th. List > nalset | Unicode version |
Description: No set contains all sets. Theorem 41 of [Suppes] p. 30. (Contributed by NM, 23-Aug-1993.) |
Ref | Expression |
---|---|
nalset |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | alexnim 1539 | . 2 | |
2 | ax-sep 3875 | . . 3 | |
3 | elequ1 1600 | . . . . . 6 | |
4 | elequ1 1600 | . . . . . . 7 | |
5 | elequ1 1600 | . . . . . . . . 9 | |
6 | elequ2 1601 | . . . . . . . . 9 | |
7 | 5, 6 | bitrd 177 | . . . . . . . 8 |
8 | 7 | notbid 592 | . . . . . . 7 |
9 | 4, 8 | anbi12d 442 | . . . . . 6 |
10 | 3, 9 | bibi12d 224 | . . . . 5 |
11 | 10 | spv 1740 | . . . 4 |
12 | pclem6 1265 | . . . 4 | |
13 | 11, 12 | syl 14 | . . 3 |
14 | 2, 13 | eximii 1493 | . 2 |
15 | 1, 14 | mpg 1340 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wa 97 wb 98 wal 1241 wex 1381 |
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-5 1336 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-4 1400 ax-13 1404 ax-14 1405 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-sep 3875 |
This theorem depends on definitions: df-bi 110 df-tru 1246 df-fal 1249 df-nf 1350 |
This theorem is referenced by: vprc 3888 |
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