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Mirrors > Home > ILE Home > Th. List > euf | Unicode version |
Description: A version of the existential uniqueness definition with a hypothesis instead of a distinct variable condition. (Contributed by NM, 12-Aug-1993.) |
Ref | Expression |
---|---|
euf.1 |
Ref | Expression |
---|---|
euf |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-eu 2016 | . 2 | |
2 | euf.1 | . . . . 5 | |
3 | ax-17 1513 | . . . . 5 | |
4 | 2, 3 | hbbi 1535 | . . . 4 |
5 | 4 | hbal 1464 | . . 3 |
6 | ax-17 1513 | . . 3 | |
7 | equequ2 1700 | . . . . 5 | |
8 | 7 | bibi2d 231 | . . . 4 |
9 | 8 | albidv 1811 | . . 3 |
10 | 5, 6, 9 | cbvexh 1742 | . 2 |
11 | 1, 10 | bitri 183 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 104 wal 1340 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-5 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 |
This theorem depends on definitions: df-bi 116 df-eu 2016 |
This theorem is referenced by: eu1 2038 eumo0 2044 |
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