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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 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ssel 3141 | . . 3 | |
2 | 1 | ad2antrr 485 | . 2 |
3 | df-rex 2454 | . . . . . 6 | |
4 | df-reu 2455 | . . . . . 6 | |
5 | 3, 4 | anbi12i 457 | . . . . 5 |
6 | 1 | ancrd 324 | . . . . . . . . . . 11 |
7 | 6 | anim1d 334 | . . . . . . . . . 10 |
8 | an32 557 | . . . . . . . . . 10 | |
9 | 7, 8 | syl6ib 160 | . . . . . . . . 9 |
10 | 9 | eximdv 1873 | . . . . . . . 8 |
11 | eupick 2098 | . . . . . . . . 9 | |
12 | 11 | ex 114 | . . . . . . . 8 |
13 | 10, 12 | syl9 72 | . . . . . . 7 |
14 | 13 | com23 78 | . . . . . 6 |
15 | 14 | imp32 255 | . . . . 5 |
16 | 5, 15 | sylan2b 285 | . . . 4 |
17 | 16 | expcomd 1434 | . . 3 |
18 | 17 | imp 123 | . 2 |
19 | 2, 18 | impbid 128 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wex 1485 weu 2019 wcel 2141 wrex 2449 wreu 2450 wss 3121 |
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 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-ext 2152 |
This theorem depends on definitions: df-bi 116 df-nf 1454 df-sb 1756 df-eu 2022 df-mo 2023 df-clab 2157 df-cleq 2163 df-clel 2166 df-rex 2454 df-reu 2455 df-in 3127 df-ss 3134 |
This theorem is referenced by: supelti 6977 |
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