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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 2939 | . . 3 | |
2 | 1 | ad2antrr 457 | . 2 |
3 | df-rex 2312 | . . . . . 6 | |
4 | df-reu 2313 | . . . . . 6 | |
5 | 3, 4 | anbi12i 433 | . . . . 5 |
6 | 1 | ancrd 309 | . . . . . . . . . . 11 |
7 | 6 | anim1d 319 | . . . . . . . . . 10 |
8 | an32 496 | . . . . . . . . . 10 | |
9 | 7, 8 | syl6ib 150 | . . . . . . . . 9 |
10 | 9 | eximdv 1760 | . . . . . . . 8 |
11 | eupick 1979 | . . . . . . . . 9 | |
12 | 11 | ex 108 | . . . . . . . 8 |
13 | 10, 12 | syl9 66 | . . . . . . 7 |
14 | 13 | com23 72 | . . . . . 6 |
15 | 14 | imp32 244 | . . . . 5 |
16 | 5, 15 | sylan2b 271 | . . . 4 |
17 | 16 | expcomd 1330 | . . 3 |
18 | 17 | imp 115 | . 2 |
19 | 2, 18 | impbid 120 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 wb 98 wex 1381 wcel 1393 weu 1900 wrex 2307 wreu 2308 wss 2917 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 |
This theorem depends on definitions: df-bi 110 df-nf 1350 df-sb 1646 df-eu 1903 df-mo 1904 df-clab 2027 df-cleq 2033 df-clel 2036 df-rex 2312 df-reu 2313 df-in 2924 df-ss 2931 |
This theorem is referenced by: (None) |
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