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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 1641 | . 2 | |
2 | ax-sep 4105 | . . 3 | |
3 | elequ1 2145 | . . . . . 6 | |
4 | elequ1 2145 | . . . . . . 7 | |
5 | elequ1 2145 | . . . . . . . . 9 | |
6 | elequ2 2146 | . . . . . . . . 9 | |
7 | 5, 6 | bitrd 187 | . . . . . . . 8 |
8 | 7 | notbid 662 | . . . . . . 7 |
9 | 4, 8 | anbi12d 470 | . . . . . 6 |
10 | 3, 9 | bibi12d 234 | . . . . 5 |
11 | 10 | spv 1853 | . . . 4 |
12 | pclem6 1369 | . . . 4 | |
13 | 11, 12 | syl 14 | . . 3 |
14 | 2, 13 | eximii 1595 | . 2 |
15 | 1, 14 | mpg 1444 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wa 103 wb 104 wal 1346 wex 1485 |
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 609 ax-in2 610 ax-5 1440 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-13 2143 ax-14 2144 ax-sep 4105 |
This theorem depends on definitions: df-bi 116 df-tru 1351 df-fal 1354 df-nf 1454 |
This theorem is referenced by: vnex 4118 |
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