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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 1498 | . . . 4 | |
2 | sp 1498 | . . . 4 | |
3 | eqtr3 2184 | . . . 4 | |
4 | 1, 2, 3 | syl2an 287 | . . 3 |
5 | 4 | gen2 1437 | . 2 |
6 | eqeq1 2171 | . . . 4 | |
7 | 6 | albidv 1811 | . . 3 |
8 | 7 | eu4 2075 | . 2 |
9 | 5, 8 | mpbiran2 930 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wal 1340 wceq 1342 wex 1479 weu 2013 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 699 ax-5 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-10 1492 ax-11 1493 ax-i12 1494 ax-bndl 1496 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-ext 2146 |
This theorem depends on definitions: df-bi 116 df-nf 1448 df-sb 1750 df-eu 2016 df-mo 2017 df-cleq 2157 |
This theorem is referenced by: eusvnfb 4427 |
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