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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 1579 | . 2 | |
2 | ax-sep 3896 | . . 3 | |
3 | elequ1 1640 | . . . . . 6 | |
4 | elequ1 1640 | . . . . . . 7 | |
5 | elequ1 1640 | . . . . . . . . 9 | |
6 | elequ2 1641 | . . . . . . . . 9 | |
7 | 5, 6 | bitrd 186 | . . . . . . . 8 |
8 | 7 | notbid 624 | . . . . . . 7 |
9 | 4, 8 | anbi12d 456 | . . . . . 6 |
10 | 3, 9 | bibi12d 233 | . . . . 5 |
11 | 10 | spv 1781 | . . . 4 |
12 | pclem6 1305 | . . . 4 | |
13 | 11, 12 | syl 14 | . . 3 |
14 | 2, 13 | eximii 1533 | . 2 |
15 | 1, 14 | mpg 1380 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wa 102 wb 103 wal 1282 wex 1421 |
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-5 1376 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-4 1440 ax-13 1444 ax-14 1445 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-sep 3896 |
This theorem depends on definitions: df-bi 115 df-tru 1287 df-fal 1290 df-nf 1390 |
This theorem is referenced by: vprc 3909 |
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