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Mirrors > Home > ILE Home > Th. List > reu8 | Unicode version |
Description: Restricted uniqueness using implicit substitution. (Contributed by NM, 24-Oct-2006.) |
Ref | Expression |
---|---|
rmo4.1 |
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Ref | Expression |
---|---|
reu8 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | rmo4.1 |
. . 3
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2 | 1 | cbvreuv 2535 |
. 2
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3 | reu6 2730 |
. 2
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4 | dfbi2 368 |
. . . . 5
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5 | 4 | ralbii 2330 |
. . . 4
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6 | ancom 253 |
. . . . . 6
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7 | equcom 1593 |
. . . . . . . . . 10
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8 | 7 | imbi2i 215 |
. . . . . . . . 9
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9 | 8 | ralbii 2330 |
. . . . . . . 8
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10 | 9 | a1i 9 |
. . . . . . 7
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11 | biimt 230 |
. . . . . . . 8
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12 | df-ral 2311 |
. . . . . . . . 9
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13 | bi2.04 237 |
. . . . . . . . . 10
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14 | 13 | albii 1359 |
. . . . . . . . 9
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15 | vex 2560 |
. . . . . . . . . 10
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16 | eleq1 2100 |
. . . . . . . . . . . . 13
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17 | 16, 1 | imbi12d 223 |
. . . . . . . . . . . 12
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
18 | 17 | bicomd 129 |
. . . . . . . . . . 11
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19 | 18 | equcoms 1594 |
. . . . . . . . . 10
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20 | 15, 19 | ceqsalv 2584 |
. . . . . . . . 9
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21 | 12, 14, 20 | 3bitrri 196 |
. . . . . . . 8
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
22 | 11, 21 | syl6bb 185 |
. . . . . . 7
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
23 | 10, 22 | anbi12d 442 |
. . . . . 6
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24 | 6, 23 | syl5bb 181 |
. . . . 5
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25 | r19.26 2441 |
. . . . 5
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26 | 24, 25 | syl6rbbr 188 |
. . . 4
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27 | 5, 26 | syl5bb 181 |
. . 3
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28 | 27 | rexbiia 2339 |
. 2
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29 | 2, 3, 28 | 3bitri 195 |
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-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 |
This theorem depends on definitions: df-bi 110 df-tru 1246 df-nf 1350 df-sb 1646 df-eu 1903 df-clab 2027 df-cleq 2033 df-clel 2036 df-ral 2311 df-rex 2312 df-reu 2313 df-v 2559 |
This theorem is referenced by: (None) |
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