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Mirrors > Home > ILE Home > Th. List > dcextest | Unicode version |
Description: If it is decidable
whether ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Ref | Expression |
---|---|
dcextest.ex |
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Ref | Expression |
---|---|
dcextest |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dcextest.ex |
. . . 4
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2 | exmiddc 822 |
. . . 4
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3 | 1, 2 | ax-mp 5 |
. . 3
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4 | vprc 4068 |
. . . . . . 7
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5 | df-v 2691 |
. . . . . . . . 9
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6 | equid 1678 |
. . . . . . . . . . 11
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7 | pm5.1im 172 |
. . . . . . . . . . 11
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8 | 6, 7 | ax-mp 5 |
. . . . . . . . . 10
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9 | 8 | abbidv 2258 |
. . . . . . . . 9
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10 | 5, 9 | syl5req 2186 |
. . . . . . . 8
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11 | 10 | eleq1d 2209 |
. . . . . . 7
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12 | 4, 11 | mtbiri 665 |
. . . . . 6
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13 | 12 | con2i 617 |
. . . . 5
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14 | vex 2692 |
. . . . . . . . . 10
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15 | biidd 171 |
. . . . . . . . . 10
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16 | 14, 15 | elab 2832 |
. . . . . . . . 9
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17 | 16 | notbii 658 |
. . . . . . . 8
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18 | 17 | biimpri 132 |
. . . . . . 7
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19 | 18 | eq0rdv 3412 |
. . . . . 6
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20 | 0ex 4063 |
. . . . . 6
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21 | 19, 20 | eqeltrdi 2231 |
. . . . 5
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22 | 13, 21 | impbii 125 |
. . . 4
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23 | 22 | notbii 658 |
. . . 4
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24 | 22, 23 | orbi12i 754 |
. . 3
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25 | 3, 24 | mpbi 144 |
. 2
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26 | df-dc 821 |
. 2
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27 | 25, 26 | mpbir 145 |
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-io 699 ax-5 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-10 1484 ax-11 1485 ax-i12 1486 ax-bndl 1487 ax-4 1488 ax-13 1492 ax-14 1493 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 ax-sep 4054 ax-nul 4062 |
This theorem depends on definitions: df-bi 116 df-dc 821 df-tru 1335 df-fal 1338 df-nf 1438 df-sb 1737 df-clab 2127 df-cleq 2133 df-clel 2136 df-nfc 2271 df-v 2691 df-dif 3078 df-in 3082 df-ss 3089 df-nul 3369 |
This theorem is referenced by: (None) |
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