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Mirrors > Home > ILE Home > Th. List > exists1 | Unicode version |
Description: Two ways to express "only one thing exists." The left-hand side requires only one variable to express this. Both sides are false in set theory. (Contributed by NM, 5-Apr-2004.) |
Ref | Expression |
---|---|
exists1 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-eu 2002 | . 2 | |
2 | equid 1677 | . . . . . 6 | |
3 | 2 | tbt 246 | . . . . 5 |
4 | bicom 139 | . . . . 5 | |
5 | 3, 4 | bitri 183 | . . . 4 |
6 | 5 | albii 1446 | . . 3 |
7 | 6 | exbii 1584 | . 2 |
8 | hbae 1696 | . . 3 | |
9 | 8 | 19.9h 1622 | . 2 |
10 | 1, 7, 9 | 3bitr2i 207 | 1 |
Colors of variables: wff set class |
Syntax hints: wb 104 wal 1329 wex 1468 weu 1999 |
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 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 |
This theorem depends on definitions: df-bi 116 df-eu 2002 |
This theorem is referenced by: exists2 2096 |
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