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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 2579 | . 2 |
3 | reu6 2781 | . 2 | |
4 | dfbi2 380 | . . . . 5 | |
5 | 4 | ralbii 2372 | . . . 4 |
6 | ancom 262 | . . . . . 6 | |
7 | equcom 1633 | . . . . . . . . . 10 | |
8 | 7 | imbi2i 224 | . . . . . . . . 9 |
9 | 8 | ralbii 2372 | . . . . . . . 8 |
10 | 9 | a1i 9 | . . . . . . 7 |
11 | biimt 239 | . . . . . . . 8 | |
12 | df-ral 2353 | . . . . . . . . 9 | |
13 | bi2.04 246 | . . . . . . . . . 10 | |
14 | 13 | albii 1399 | . . . . . . . . 9 |
15 | vex 2604 | . . . . . . . . . 10 | |
16 | eleq1 2141 | . . . . . . . . . . . . 13 | |
17 | 16, 1 | imbi12d 232 | . . . . . . . . . . . 12 |
18 | 17 | bicomd 139 | . . . . . . . . . . 11 |
19 | 18 | equcoms 1634 | . . . . . . . . . 10 |
20 | 15, 19 | ceqsalv 2629 | . . . . . . . . 9 |
21 | 12, 14, 20 | 3bitrri 205 | . . . . . . . 8 |
22 | 11, 21 | syl6bb 194 | . . . . . . 7 |
23 | 10, 22 | anbi12d 456 | . . . . . 6 |
24 | 6, 23 | syl5bb 190 | . . . . 5 |
25 | r19.26 2485 | . . . . 5 | |
26 | 24, 25 | syl6rbbr 197 | . . . 4 |
27 | 5, 26 | syl5bb 190 | . . 3 |
28 | 27 | rexbiia 2381 | . 2 |
29 | 2, 3, 28 | 3bitri 204 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 102 wb 103 wal 1282 wcel 1433 wral 2348 wrex 2349 wreu 2350 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-io 662 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-10 1436 ax-11 1437 ax-i12 1438 ax-bndl 1439 ax-4 1440 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 |
This theorem depends on definitions: df-bi 115 df-tru 1287 df-nf 1390 df-sb 1686 df-eu 1944 df-clab 2068 df-cleq 2074 df-clel 2077 df-ral 2353 df-rex 2354 df-reu 2355 df-v 2603 |
This theorem is referenced by: (None) |
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