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Mirrors > Home > ILE Home > Th. List > Mathboxes > bj-nalset | Unicode version |
Description: nalset 3878 from bounded separation. (Contributed by BJ, 18-Nov-2019.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
bj-nalset |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | alexnim 1536 |
. 2
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2 | ax-bdel 9276 |
. . . . 5
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3 | 2 | ax-bdn 9272 |
. . . 4
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4 | 3 | bdsep1 9340 |
. . 3
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5 | elequ1 1597 |
. . . . . 6
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6 | elequ1 1597 |
. . . . . . 7
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7 | elequ1 1597 |
. . . . . . . . 9
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8 | elequ2 1598 |
. . . . . . . . 9
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9 | 7, 8 | bitrd 177 |
. . . . . . . 8
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10 | 9 | notbid 591 |
. . . . . . 7
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11 | 6, 10 | anbi12d 442 |
. . . . . 6
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12 | 5, 11 | bibi12d 224 |
. . . . 5
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13 | 12 | spv 1737 |
. . . 4
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14 | pclem6 1264 |
. . . 4
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15 | 13, 14 | syl 14 |
. . 3
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16 | 4, 15 | eximii 1490 |
. 2
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17 | 1, 16 | mpg 1337 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-in1 544 ax-in2 545 ax-5 1333 ax-gen 1335 ax-ie1 1379 ax-ie2 1380 ax-8 1392 ax-4 1397 ax-13 1401 ax-14 1402 ax-17 1416 ax-i9 1420 ax-ial 1424 ax-bdn 9272 ax-bdel 9276 ax-bdsep 9339 |
This theorem depends on definitions: df-bi 110 df-tru 1245 df-fal 1248 df-nf 1347 |
This theorem is referenced by: bj-vprc 9351 |
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