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Mirrors > Home > MPE Home > Th. List > nalset | Structured version Visualization version 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 | alexn 1771 | . 2 | |
2 | ax-sep 4781 | . . 3 | |
3 | elequ1 1997 | . . . . . 6 | |
4 | elequ1 1997 | . . . . . . 7 | |
5 | elequ1 1997 | . . . . . . . . 9 | |
6 | elequ2 2004 | . . . . . . . . 9 | |
7 | 5, 6 | bitrd 268 | . . . . . . . 8 |
8 | 7 | notbid 308 | . . . . . . 7 |
9 | 4, 8 | anbi12d 747 | . . . . . 6 |
10 | 3, 9 | bibi12d 335 | . . . . 5 |
11 | 10 | spv 2260 | . . . 4 |
12 | pclem6 971 | . . . 4 | |
13 | 11, 12 | syl 17 | . . 3 |
14 | 2, 13 | eximii 1764 | . 2 |
15 | 1, 14 | mpgbi 1725 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wn 3 wb 196 wa 384 wal 1481 wex 1704 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-8 1992 ax-9 1999 ax-12 2047 ax-13 2246 ax-sep 4781 |
This theorem depends on definitions: df-bi 197 df-an 386 df-ex 1705 |
This theorem is referenced by: vprc 4796 kmlem2 8973 |
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