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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 2029 |
. 2
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2 | euf.1 |
. . . . 5
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3 | ax-17 1526 |
. . . . 5
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4 | 2, 3 | hbbi 1548 |
. . . 4
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5 | 4 | hbal 1477 |
. . 3
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6 | ax-17 1526 |
. . 3
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7 | equequ2 1713 |
. . . . 5
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8 | 7 | bibi2d 232 |
. . . 4
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9 | 8 | albidv 1824 |
. . 3
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10 | 5, 6, 9 | cbvexh 1755 |
. 2
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11 | 1, 10 | bitri 184 |
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 106 ax-ia2 107 ax-ia3 108 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 |
This theorem depends on definitions: df-bi 117 df-eu 2029 |
This theorem is referenced by: eu1 2051 eumo0 2057 |
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