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Mirrors > Home > ILE Home > Th. List > eqeu | Unicode version |
Description: A condition which implies existential uniqueness. (Contributed by Jeff Hankins, 8-Sep-2009.) |
Ref | Expression |
---|---|
eqeu.1 |
Ref | Expression |
---|---|
eqeu |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqeu.1 | . . . . 5 | |
2 | 1 | spcegv 2641 | . . . 4 |
3 | 2 | imp 115 | . . 3 |
4 | 3 | 3adant3 924 | . 2 |
5 | eqeq2 2049 | . . . . . . 7 | |
6 | 5 | imbi2d 219 | . . . . . 6 |
7 | 6 | albidv 1705 | . . . . 5 |
8 | 7 | spcegv 2641 | . . . 4 |
9 | 8 | imp 115 | . . 3 |
10 | 9 | 3adant2 923 | . 2 |
11 | nfv 1421 | . . 3 | |
12 | 11 | eu3 1946 | . 2 |
13 | 4, 10, 12 | sylanbrc 394 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 98 w3a 885 wal 1241 wceq 1243 wex 1381 wcel 1393 weu 1900 |
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-3an 887 df-tru 1246 df-nf 1350 df-sb 1646 df-eu 1903 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-v 2559 |
This theorem is referenced by: (None) |
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