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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 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | alexnim 1628 |
. 2
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2 | ax-sep 4054 |
. . 3
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3 | elequ1 1691 |
. . . . . 6
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4 | elequ1 1691 |
. . . . . . 7
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5 | elequ1 1691 |
. . . . . . . . 9
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6 | elequ2 1692 |
. . . . . . . . 9
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7 | 5, 6 | bitrd 187 |
. . . . . . . 8
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8 | 7 | notbid 657 |
. . . . . . 7
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9 | 4, 8 | anbi12d 465 |
. . . . . 6
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10 | 3, 9 | bibi12d 234 |
. . . . 5
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11 | 10 | spv 1833 |
. . . 4
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12 | pclem6 1353 |
. . . 4
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13 | 11, 12 | syl 14 |
. . 3
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14 | 2, 13 | eximii 1582 |
. 2
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15 | 1, 14 | mpg 1428 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() |
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 604 ax-in2 605 ax-5 1424 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-4 1488 ax-13 1492 ax-14 1493 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-sep 4054 |
This theorem depends on definitions: df-bi 116 df-tru 1335 df-fal 1338 df-nf 1438 |
This theorem is referenced by: vnex 4067 |
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