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Mirrors > Home > ILE Home > Th. List > reupick2 | Unicode version |
Description: Restricted uniqueness "picks" a member of a subclass. (Contributed by Mario Carneiro, 15-Dec-2013.) (Proof shortened by Mario Carneiro, 19-Nov-2016.) |
Ref | Expression |
---|---|
reupick2 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ancr 319 |
. . . . . 6
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2 | 1 | ralimi 2498 |
. . . . 5
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3 | rexim 2529 |
. . . . 5
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4 | 2, 3 | syl 14 |
. . . 4
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5 | reupick3 3366 |
. . . . . 6
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6 | 5 | 3exp 1181 |
. . . . 5
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7 | 6 | com12 30 |
. . . 4
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8 | 4, 7 | syl6 33 |
. . 3
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9 | 8 | 3imp1 1199 |
. 2
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10 | rsp 2483 |
. . . 4
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11 | 10 | 3ad2ant1 1003 |
. . 3
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12 | 11 | imp 123 |
. 2
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13 | 9, 12 | 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 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-nf 1438 df-sb 1737 df-eu 2003 df-mo 2004 df-ral 2422 df-rex 2423 df-reu 2424 |
This theorem is referenced by: (None) |
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