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Mirrors > Home > MPE Home > Th. List > reupick | Structured version Visualization version 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 3597 | . . 3 | |
2 | 1 | ad2antrr 762 | . 2 |
3 | df-rex 2918 | . . . . . 6 | |
4 | df-reu 2919 | . . . . . 6 | |
5 | 3, 4 | anbi12i 733 | . . . . 5 |
6 | 1 | ancrd 577 | . . . . . . . . . . 11 |
7 | 6 | anim1d 588 | . . . . . . . . . 10 |
8 | an32 839 | . . . . . . . . . 10 | |
9 | 7, 8 | syl6ib 241 | . . . . . . . . 9 |
10 | 9 | eximdv 1846 | . . . . . . . 8 |
11 | eupick 2536 | . . . . . . . . 9 | |
12 | 11 | ex 450 | . . . . . . . 8 |
13 | 10, 12 | syl9 77 | . . . . . . 7 |
14 | 13 | com23 86 | . . . . . 6 |
15 | 14 | imp32 449 | . . . . 5 |
16 | 5, 15 | sylan2b 492 | . . . 4 |
17 | 16 | expcomd 454 | . . 3 |
18 | 17 | imp 445 | . 2 |
19 | 2, 18 | impbid 202 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 196 wa 384 wex 1704 wcel 1990 weu 2470 wrex 2913 wreu 2914 wss 3574 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-eu 2474 df-mo 2475 df-clab 2609 df-cleq 2615 df-clel 2618 df-rex 2918 df-reu 2919 df-in 3581 df-ss 3588 |
This theorem is referenced by: (None) |
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