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Mirrors > Home > MPE Home > Th. List > eunex | Structured version Visualization version Unicode version |
Description: Existential uniqueness implies there is a value for which the wff argument is false. (Contributed by NM, 24-Oct-2010.) |
Ref | Expression |
---|---|
eunex |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dtru 4593 |
. . . . 5
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2 | alim 1682 |
. . . . 5
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3 | 1, 2 | mtoi 182 |
. . . 4
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4 | 3 | exlimiv 1775 |
. . 3
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5 | 4 | adantl 468 |
. 2
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6 | eu3v 2326 |
. 2
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7 | exnal 1698 |
. 2
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8 | 5, 6, 7 | 3imtr4i 270 |
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 1668 ax-4 1681 ax-5 1757 ax-6 1804 ax-7 1850 ax-8 1888 ax-9 1895 ax-10 1914 ax-11 1919 ax-12 1932 ax-13 2090 ax-nul 4533 ax-pow 4580 |
This theorem depends on definitions: df-bi 189 df-an 373 df-tru 1446 df-ex 1663 df-nf 1667 df-eu 2302 df-mo 2303 |
This theorem is referenced by: reusv2lem2 4604 unnt 31061 amosym1 31079 alneu 38616 |
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