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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 2720 |
. 2
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3 | reu6 2941 |
. 2
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4 | dfbi2 388 |
. . . . 5
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5 | 4 | ralbii 2496 |
. . . 4
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6 | r19.26 2616 |
. . . . 5
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7 | ancom 266 |
. . . . . 6
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8 | equcom 1717 |
. . . . . . . . . 10
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9 | 8 | imbi2i 226 |
. . . . . . . . 9
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10 | 9 | ralbii 2496 |
. . . . . . . 8
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11 | 10 | a1i 9 |
. . . . . . 7
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12 | biimt 241 |
. . . . . . . 8
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13 | df-ral 2473 |
. . . . . . . . 9
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14 | bi2.04 248 |
. . . . . . . . . 10
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15 | 14 | albii 1481 |
. . . . . . . . 9
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16 | vex 2755 |
. . . . . . . . . 10
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17 | eleq1 2252 |
. . . . . . . . . . . . 13
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18 | 17, 1 | imbi12d 234 |
. . . . . . . . . . . 12
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19 | 18 | bicomd 141 |
. . . . . . . . . . 11
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20 | 19 | equcoms 1719 |
. . . . . . . . . 10
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21 | 16, 20 | ceqsalv 2782 |
. . . . . . . . 9
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22 | 13, 15, 21 | 3bitrri 207 |
. . . . . . . 8
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23 | 12, 22 | bitrdi 196 |
. . . . . . 7
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24 | 11, 23 | anbi12d 473 |
. . . . . 6
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25 | 7, 24 | bitrid 192 |
. . . . 5
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26 | 6, 25 | bitr4id 199 |
. . . 4
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27 | 5, 26 | bitrid 192 |
. . 3
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28 | 27 | rexbiia 2505 |
. 2
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29 | 2, 3, 28 | 3bitri 206 |
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-io 710 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-10 1516 ax-11 1517 ax-i12 1518 ax-bndl 1520 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-ext 2171 |
This theorem depends on definitions: df-bi 117 df-tru 1367 df-nf 1472 df-sb 1774 df-eu 2041 df-clab 2176 df-cleq 2182 df-clel 2185 df-ral 2473 df-rex 2474 df-reu 2475 df-v 2754 |
This theorem is referenced by: updjud 7111 reumodprminv 12285 grpinveu 12982 |
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