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Mirrors > Home > MPE Home > Th. List > euf | Structured version Visualization version 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.) (Proof shortened by Wolf Lammen, 30-Oct-2018.) |
Ref | Expression |
---|---|
euf.1 |
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Ref | Expression |
---|---|
euf |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-eu 2314 |
. 2
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2 | euf.1 |
. . . . 5
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3 | nfv 1772 |
. . . . 5
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4 | 2, 3 | nfbi 2028 |
. . . 4
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5 | 4 | nfal 2041 |
. . 3
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6 | nfv 1772 |
. . 3
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7 | equequ2 1879 |
. . . . 5
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8 | 7 | bibi2d 324 |
. . . 4
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9 | 8 | albidv 1778 |
. . 3
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10 | 5, 6, 9 | cbvex 2126 |
. 2
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11 | 1, 10 | bitri 257 |
1
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Colors of variables: wff setvar class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1680 ax-4 1693 ax-5 1769 ax-6 1816 ax-7 1862 ax-10 1926 ax-11 1931 ax-12 1944 ax-13 2102 |
This theorem depends on definitions: df-bi 190 df-an 377 df-tru 1458 df-ex 1675 df-nf 1679 df-eu 2314 |
This theorem is referenced by: eu1 2350 bj-eumo0 31488 |
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