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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 321 |
. . . . . 6
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2 | 1 | ralimi 2553 |
. . . . 5
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3 | rexim 2584 |
. . . . 5
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4 | 2, 3 | syl 14 |
. . . 4
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5 | reupick3 3435 |
. . . . . 6
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6 | 5 | 3exp 1204 |
. . . . 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 1222 |
. 2
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10 | rsp 2537 |
. . . 4
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11 | 10 | 3ad2ant1 1020 |
. . 3
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12 | 11 | imp 124 |
. 2
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13 | 9, 12 | impbid 129 |
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 106 ax-ia2 107 ax-ia3 108 ax-io 710 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-10 1516 ax-11 1517 ax-i12 1518 ax-bndl 1520 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 |
This theorem depends on definitions: df-bi 117 df-3an 982 df-nf 1472 df-sb 1774 df-eu 2041 df-mo 2042 df-ral 2473 df-rex 2474 df-reu 2475 |
This theorem is referenced by: (None) |
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