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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 |
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Ref | Expression |
---|---|
euf |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-eu 1900 |
. 2
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2 | euf.1 |
. . . . 5
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3 | ax-17 1416 |
. . . . 5
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4 | 2, 3 | hbbi 1437 |
. . . 4
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5 | 4 | hbal 1363 |
. . 3
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6 | ax-17 1416 |
. . 3
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7 | equequ2 1596 |
. . . . 5
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8 | 7 | bibi2d 221 |
. . . 4
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9 | 8 | albidv 1702 |
. . 3
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10 | 5, 6, 9 | cbvexh 1635 |
. 2
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11 | 1, 10 | bitri 173 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() |
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-5 1333 ax-7 1334 ax-gen 1335 ax-ie1 1379 ax-ie2 1380 ax-8 1392 ax-4 1397 ax-17 1416 ax-i9 1420 ax-ial 1424 ax-i5r 1425 |
This theorem depends on definitions: df-bi 110 df-eu 1900 |
This theorem is referenced by: eu1 1922 eumo0 1928 |
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