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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 837 |
. . . 4
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3 | 1, 2 | ax-mp 5 |
. . 3
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4 | vprc 4147 |
. . . . . . 7
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5 | df-v 2751 |
. . . . . . . . 9
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6 | equid 1711 |
. . . . . . . . . . 11
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7 | pm5.1im 173 |
. . . . . . . . . . 11
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8 | 6, 7 | ax-mp 5 |
. . . . . . . . . 10
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9 | 8 | abbidv 2305 |
. . . . . . . . 9
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10 | 5, 9 | eqtr2id 2233 |
. . . . . . . 8
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11 | 10 | eleq1d 2256 |
. . . . . . 7
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12 | 4, 11 | mtbiri 676 |
. . . . . 6
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13 | 12 | con2i 628 |
. . . . 5
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14 | vex 2752 |
. . . . . . . . . 10
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15 | biidd 172 |
. . . . . . . . . 10
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16 | 14, 15 | elab 2893 |
. . . . . . . . 9
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17 | 16 | notbii 669 |
. . . . . . . 8
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18 | 17 | biimpri 133 |
. . . . . . 7
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19 | 18 | eq0rdv 3479 |
. . . . . 6
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20 | 0ex 4142 |
. . . . . 6
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21 | 19, 20 | eqeltrdi 2278 |
. . . . 5
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22 | 13, 21 | impbii 126 |
. . . 4
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23 | 22 | notbii 669 |
. . . 4
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24 | 22, 23 | orbi12i 765 |
. . 3
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25 | 3, 24 | mpbi 145 |
. 2
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26 | df-dc 836 |
. 2
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27 | 25, 26 | mpbir 146 |
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-io 710 ax-5 1457 ax-7 1458 ax-gen 1459 ax-ie1 1503 ax-ie2 1504 ax-8 1514 ax-10 1515 ax-11 1516 ax-i12 1517 ax-bndl 1519 ax-4 1520 ax-17 1536 ax-i9 1540 ax-ial 1544 ax-i5r 1545 ax-13 2160 ax-14 2161 ax-ext 2169 ax-sep 4133 ax-nul 4141 |
This theorem depends on definitions: df-bi 117 df-dc 836 df-tru 1366 df-fal 1369 df-nf 1471 df-sb 1773 df-clab 2174 df-cleq 2180 df-clel 2183 df-nfc 2318 df-v 2751 df-dif 3143 df-in 3147 df-ss 3154 df-nul 3435 |
This theorem is referenced by: (None) |
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