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Mirrors > Home > NFE Home > Th. List > eqeu | Unicode version |
Description: A condition which implies existential uniqueness. (Contributed by Jeff Hankins, 8-Sep-2009.) |
Ref | Expression |
---|---|
eqeu.1 |
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Ref | Expression |
---|---|
eqeu |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqeu.1 |
. . . . 5
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2 | 1 | spcegv 2941 |
. . . 4
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3 | 2 | imp 418 |
. . 3
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4 | 3 | 3adant3 975 |
. 2
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5 | eqeq2 2362 |
. . . . . . 7
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6 | 5 | imbi2d 307 |
. . . . . 6
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7 | 6 | albidv 1625 |
. . . . 5
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8 | 7 | spcegv 2941 |
. . . 4
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9 | 8 | imp 418 |
. . 3
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10 | 9 | 3adant2 974 |
. 2
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11 | nfv 1619 |
. . 3
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12 | 11 | eu3 2230 |
. 2
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13 | 4, 10, 12 | sylanbrc 645 |
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 1546 ax-5 1557 ax-17 1616 ax-9 1654 ax-8 1675 ax-6 1729 ax-7 1734 ax-11 1746 ax-12 1925 ax-ext 2334 |
This theorem depends on definitions: df-bi 177 df-or 359 df-an 360 df-3an 936 df-tru 1319 df-ex 1542 df-nf 1545 df-sb 1649 df-eu 2208 df-clab 2340 df-cleq 2346 df-clel 2349 df-nfc 2479 df-v 2862 |
This theorem is referenced by: (None) |
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