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Mirrors > Home > ILE Home > Th. List > reu7 | Unicode version |
Description: Restricted uniqueness using implicit substitution. (Contributed by NM, 24-Oct-2006.) |
Ref | Expression |
---|---|
rmo4.1 |
Ref | Expression |
---|---|
reu7 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | reu3 2731 | . 2 | |
2 | rmo4.1 | . . . . . . 7 | |
3 | equequ1 1598 | . . . . . . . 8 | |
4 | equcom 1593 | . . . . . . . 8 | |
5 | 3, 4 | syl6bb 185 | . . . . . . 7 |
6 | 2, 5 | imbi12d 223 | . . . . . 6 |
7 | 6 | cbvralv 2533 | . . . . 5 |
8 | 7 | rexbii 2331 | . . . 4 |
9 | equequ1 1598 | . . . . . . 7 | |
10 | 9 | imbi2d 219 | . . . . . 6 |
11 | 10 | ralbidv 2326 | . . . . 5 |
12 | 11 | cbvrexv 2534 | . . . 4 |
13 | 8, 12 | bitri 173 | . . 3 |
14 | 13 | anbi2i 430 | . 2 |
15 | 1, 14 | bitri 173 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 wb 98 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-mo 1904 df-cleq 2033 df-clel 2036 df-nfc 2167 df-ral 2311 df-rex 2312 df-reu 2313 df-rmo 2314 |
This theorem is referenced by: (None) |
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