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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 |
Ref | Expression |
---|---|
reu8 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | rmo4.1 | . . 3 | |
2 | 1 | cbvreuv 2698 | . 2 |
3 | reu6 2919 | . 2 | |
4 | dfbi2 386 | . . . . 5 | |
5 | 4 | ralbii 2476 | . . . 4 |
6 | r19.26 2596 | . . . . 5 | |
7 | ancom 264 | . . . . . 6 | |
8 | equcom 1699 | . . . . . . . . . 10 | |
9 | 8 | imbi2i 225 | . . . . . . . . 9 |
10 | 9 | ralbii 2476 | . . . . . . . 8 |
11 | 10 | a1i 9 | . . . . . . 7 |
12 | biimt 240 | . . . . . . . 8 | |
13 | df-ral 2453 | . . . . . . . . 9 | |
14 | bi2.04 247 | . . . . . . . . . 10 | |
15 | 14 | albii 1463 | . . . . . . . . 9 |
16 | vex 2733 | . . . . . . . . . 10 | |
17 | eleq1 2233 | . . . . . . . . . . . . 13 | |
18 | 17, 1 | imbi12d 233 | . . . . . . . . . . . 12 |
19 | 18 | bicomd 140 | . . . . . . . . . . 11 |
20 | 19 | equcoms 1701 | . . . . . . . . . 10 |
21 | 16, 20 | ceqsalv 2760 | . . . . . . . . 9 |
22 | 13, 15, 21 | 3bitrri 206 | . . . . . . . 8 |
23 | 12, 22 | bitrdi 195 | . . . . . . 7 |
24 | 11, 23 | anbi12d 470 | . . . . . 6 |
25 | 7, 24 | syl5bb 191 | . . . . 5 |
26 | 6, 25 | bitr4id 198 | . . . 4 |
27 | 5, 26 | syl5bb 191 | . . 3 |
28 | 27 | rexbiia 2485 | . 2 |
29 | 2, 3, 28 | 3bitri 205 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wal 1346 wcel 2141 wral 2448 wrex 2449 wreu 2450 |
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 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-ext 2152 |
This theorem depends on definitions: df-bi 116 df-tru 1351 df-nf 1454 df-sb 1756 df-eu 2022 df-clab 2157 df-cleq 2163 df-clel 2166 df-ral 2453 df-rex 2454 df-reu 2455 df-v 2732 |
This theorem is referenced by: updjud 7055 reumodprminv 12194 grpinveu 12728 |
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