Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
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 1627 | . 2 | |
2 | ax-sep 4046 | . . 3 | |
3 | elequ1 1690 | . . . . . 6 | |
4 | elequ1 1690 | . . . . . . 7 | |
5 | elequ1 1690 | . . . . . . . . 9 | |
6 | elequ2 1691 | . . . . . . . . 9 | |
7 | 5, 6 | bitrd 187 | . . . . . . . 8 |
8 | 7 | notbid 656 | . . . . . . 7 |
9 | 4, 8 | anbi12d 464 | . . . . . 6 |
10 | 3, 9 | bibi12d 234 | . . . . 5 |
11 | 10 | spv 1832 | . . . 4 |
12 | pclem6 1352 | . . . 4 | |
13 | 11, 12 | syl 14 | . . 3 |
14 | 2, 13 | eximii 1581 | . 2 |
15 | 1, 14 | mpg 1427 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wa 103 wb 104 wal 1329 wex 1468 |
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-5 1423 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-4 1487 ax-13 1491 ax-14 1492 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-sep 4046 |
This theorem depends on definitions: df-bi 116 df-tru 1334 df-fal 1337 df-nf 1437 |
This theorem is referenced by: vnex 4059 |
Copyright terms: Public domain | W3C validator |