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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 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-eu 2003 |
. 2
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2 | equid 1678 |
. . . . . 6
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3 | 2 | tbt 246 |
. . . . 5
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4 | bicom 139 |
. . . . 5
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5 | 3, 4 | bitri 183 |
. . . 4
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6 | 5 | albii 1447 |
. . 3
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7 | 6 | exbii 1585 |
. 2
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8 | hbae 1697 |
. . 3
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9 | 8 | 19.9h 1623 |
. 2
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10 | 1, 7, 9 | 3bitr2i 207 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() |
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 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-10 1484 ax-11 1485 ax-i12 1486 ax-4 1488 ax-17 1507 ax-i9 1511 ax-ial 1515 |
This theorem depends on definitions: df-bi 116 df-eu 2003 |
This theorem is referenced by: exists2 2097 |
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