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Mirrors > Home > ILE Home > Th. List > eusv1 | Unicode version |
Description: Two ways to express single-valuedness of a class expression . (Contributed by NM, 14-Oct-2010.) |
Ref | Expression |
---|---|
eusv1 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sp 1401 | . . . 4 | |
2 | sp 1401 | . . . 4 | |
3 | eqtr3 2059 | . . . 4 | |
4 | 1, 2, 3 | syl2an 273 | . . 3 |
5 | 4 | gen2 1339 | . 2 |
6 | eqeq1 2046 | . . . 4 | |
7 | 6 | albidv 1705 | . . 3 |
8 | 7 | eu4 1962 | . 2 |
9 | 5, 8 | mpbiran2 848 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 wb 98 wal 1241 wceq 1243 wex 1381 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-nf 1350 df-sb 1646 df-eu 1903 df-mo 1904 df-cleq 2033 |
This theorem is referenced by: eusvnfb 4186 |
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