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Mirrors > Home > ILE Home > Th. List > reupick | 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 3096 |
. . 3
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2 | 1 | ad2antrr 480 |
. 2
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3 | df-rex 2423 |
. . . . . 6
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4 | df-reu 2424 |
. . . . . 6
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5 | 3, 4 | anbi12i 456 |
. . . . 5
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6 | 1 | ancrd 324 |
. . . . . . . . . . 11
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7 | 6 | anim1d 334 |
. . . . . . . . . 10
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8 | an32 552 |
. . . . . . . . . 10
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9 | 7, 8 | syl6ib 160 |
. . . . . . . . 9
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10 | 9 | eximdv 1853 |
. . . . . . . 8
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11 | eupick 2079 |
. . . . . . . . 9
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12 | 11 | ex 114 |
. . . . . . . 8
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13 | 10, 12 | syl9 72 |
. . . . . . 7
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14 | 13 | com23 78 |
. . . . . 6
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15 | 14 | imp32 255 |
. . . . 5
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16 | 5, 15 | sylan2b 285 |
. . . 4
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17 | 16 | expcomd 1418 |
. . 3
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18 | 17 | imp 123 |
. 2
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19 | 2, 18 | impbid 128 |
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 105 ax-ia2 106 ax-ia3 107 ax-io 699 ax-5 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-10 1484 ax-11 1485 ax-i12 1486 ax-bndl 1487 ax-4 1488 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 |
This theorem depends on definitions: df-bi 116 df-nf 1438 df-sb 1737 df-eu 2003 df-mo 2004 df-clab 2127 df-cleq 2133 df-clel 2136 df-rex 2423 df-reu 2424 df-in 3082 df-ss 3089 |
This theorem is referenced by: supelti 6897 |
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