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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 2659 |
. 2
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3 | reu6 2877 |
. 2
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4 | dfbi2 386 |
. . . . 5
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5 | 4 | ralbii 2444 |
. . . 4
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6 | r19.26 2561 |
. . . . 5
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7 | ancom 264 |
. . . . . 6
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8 | equcom 1683 |
. . . . . . . . . 10
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9 | 8 | imbi2i 225 |
. . . . . . . . 9
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10 | 9 | ralbii 2444 |
. . . . . . . 8
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11 | 10 | a1i 9 |
. . . . . . 7
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12 | biimt 240 |
. . . . . . . 8
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13 | df-ral 2422 |
. . . . . . . . 9
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14 | bi2.04 247 |
. . . . . . . . . 10
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15 | 14 | albii 1447 |
. . . . . . . . 9
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16 | vex 2692 |
. . . . . . . . . 10
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17 | eleq1 2203 |
. . . . . . . . . . . . 13
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18 | 17, 1 | imbi12d 233 |
. . . . . . . . . . . 12
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19 | 18 | bicomd 140 |
. . . . . . . . . . 11
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20 | 19 | equcoms 1685 |
. . . . . . . . . 10
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21 | 16, 20 | ceqsalv 2719 |
. . . . . . . . 9
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22 | 13, 15, 21 | 3bitrri 206 |
. . . . . . . 8
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23 | 12, 22 | syl6bb 195 |
. . . . . . 7
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24 | 11, 23 | anbi12d 465 |
. . . . . 6
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25 | 7, 24 | syl5bb 191 |
. . . . 5
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26 | 6, 25 | bitr4id 198 |
. . . 4
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27 | 5, 26 | syl5bb 191 |
. . 3
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28 | 27 | rexbiia 2453 |
. 2
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29 | 2, 3, 28 | 3bitri 205 |
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-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-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 |
This theorem depends on definitions: df-bi 116 df-tru 1335 df-nf 1438 df-sb 1737 df-eu 2003 df-clab 2127 df-cleq 2133 df-clel 2136 df-ral 2422 df-rex 2423 df-reu 2424 df-v 2691 |
This theorem is referenced by: updjud 6975 |
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