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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 2535 | . 2 |
3 | reu6 2730 | . 2 | |
4 | dfbi2 368 | . . . . 5 | |
5 | 4 | ralbii 2330 | . . . 4 |
6 | ancom 253 | . . . . . 6 | |
7 | equcom 1593 | . . . . . . . . . 10 | |
8 | 7 | imbi2i 215 | . . . . . . . . 9 |
9 | 8 | ralbii 2330 | . . . . . . . 8 |
10 | 9 | a1i 9 | . . . . . . 7 |
11 | biimt 230 | . . . . . . . 8 | |
12 | df-ral 2311 | . . . . . . . . 9 | |
13 | bi2.04 237 | . . . . . . . . . 10 | |
14 | 13 | albii 1359 | . . . . . . . . 9 |
15 | vex 2560 | . . . . . . . . . 10 | |
16 | eleq1 2100 | . . . . . . . . . . . . 13 | |
17 | 16, 1 | imbi12d 223 | . . . . . . . . . . . 12 |
18 | 17 | bicomd 129 | . . . . . . . . . . 11 |
19 | 18 | equcoms 1594 | . . . . . . . . . 10 |
20 | 15, 19 | ceqsalv 2584 | . . . . . . . . 9 |
21 | 12, 14, 20 | 3bitrri 196 | . . . . . . . 8 |
22 | 11, 21 | syl6bb 185 | . . . . . . 7 |
23 | 10, 22 | anbi12d 442 | . . . . . 6 |
24 | 6, 23 | syl5bb 181 | . . . . 5 |
25 | r19.26 2441 | . . . . 5 | |
26 | 24, 25 | syl6rbbr 188 | . . . 4 |
27 | 5, 26 | syl5bb 181 | . . 3 |
28 | 27 | rexbiia 2339 | . 2 |
29 | 2, 3, 28 | 3bitri 195 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 wb 98 wal 1241 wcel 1393 wral 2306 wrex 2307 wreu 2308 |
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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