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Mirrors > Home > MPE Home > Th. List > reupick | Structured version Visualization version Unicode version |
Description: Restricted uniqueness "picks" a member of a subclass. (Contributed by NM, 21-Aug-1999.) |
Ref | Expression |
---|---|
reupick |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ssel 3426 |
. . 3
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2 | 1 | ad2antrr 732 |
. 2
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3 | df-rex 2743 |
. . . . . 6
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4 | df-reu 2744 |
. . . . . 6
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5 | 3, 4 | anbi12i 703 |
. . . . 5
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6 | 1 | ancrd 557 |
. . . . . . . . . . 11
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7 | 6 | anim1d 568 |
. . . . . . . . . 10
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8 | an32 807 |
. . . . . . . . . 10
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9 | 7, 8 | syl6ib 230 |
. . . . . . . . 9
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10 | 9 | eximdv 1764 |
. . . . . . . 8
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11 | eupick 2365 |
. . . . . . . . 9
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12 | 11 | ex 436 |
. . . . . . . 8
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13 | 10, 12 | syl9 73 |
. . . . . . 7
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14 | 13 | com23 81 |
. . . . . 6
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15 | 14 | imp32 435 |
. . . . 5
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16 | 5, 15 | sylan2b 478 |
. . . 4
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17 | 16 | expcomd 440 |
. . 3
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18 | 17 | imp 431 |
. 2
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19 | 2, 18 | impbid 194 |
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 1669 ax-4 1682 ax-5 1758 ax-6 1805 ax-7 1851 ax-10 1915 ax-11 1920 ax-12 1933 ax-13 2091 ax-ext 2431 |
This theorem depends on definitions: df-bi 189 df-an 373 df-tru 1447 df-ex 1664 df-nf 1668 df-sb 1798 df-eu 2303 df-mo 2304 df-clab 2438 df-cleq 2444 df-clel 2447 df-rex 2743 df-reu 2744 df-in 3411 df-ss 3418 |
This theorem is referenced by: (None) |
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