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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 1659 |
. 2
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2 | ax-sep 4136 |
. . 3
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3 | elequ1 2164 |
. . . . . 6
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4 | elequ1 2164 |
. . . . . . 7
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5 | elequ1 2164 |
. . . . . . . . 9
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6 | elequ2 2165 |
. . . . . . . . 9
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7 | 5, 6 | bitrd 188 |
. . . . . . . 8
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8 | 7 | notbid 668 |
. . . . . . 7
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9 | 4, 8 | anbi12d 473 |
. . . . . 6
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10 | 3, 9 | bibi12d 235 |
. . . . 5
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11 | 10 | spv 1871 |
. . . 4
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12 | pclem6 1385 |
. . . 4
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13 | 11, 12 | syl 14 |
. . 3
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14 | 2, 13 | eximii 1613 |
. 2
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15 | 1, 14 | mpg 1462 |
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 106 ax-ia2 107 ax-ia3 108 ax-in1 615 ax-in2 616 ax-5 1458 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-13 2162 ax-14 2163 ax-sep 4136 |
This theorem depends on definitions: df-bi 117 df-tru 1367 df-fal 1370 df-nf 1472 |
This theorem is referenced by: vnex 4149 |
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