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Mirrors > Home > ILE Home > Th. List > mopick | Unicode version |
Description: "At most one" picks a variable value, eliminating an existential quantifier. (Contributed by NM, 27-Jan-1997.) |
Ref | Expression |
---|---|
mopick |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax-17 1419 | . . . 4 | |
2 | hbs1 1814 | . . . . 5 | |
3 | hbs1 1814 | . . . . 5 | |
4 | 2, 3 | hban 1439 | . . . 4 |
5 | sbequ12 1654 | . . . . 5 | |
6 | sbequ12 1654 | . . . . 5 | |
7 | 5, 6 | anbi12d 442 | . . . 4 |
8 | 1, 4, 7 | cbvexh 1638 | . . 3 |
9 | ax-17 1419 | . . . . . . 7 | |
10 | 9 | mo3h 1953 | . . . . . 6 |
11 | ax-4 1400 | . . . . . . 7 | |
12 | 11 | sps 1430 | . . . . . 6 |
13 | 10, 12 | sylbi 114 | . . . . 5 |
14 | sbequ2 1652 | . . . . . . . . 9 | |
15 | 14 | imim2i 12 | . . . . . . . 8 |
16 | 15 | expd 245 | . . . . . . 7 |
17 | 16 | com4t 79 | . . . . . 6 |
18 | 17 | imp 115 | . . . . 5 |
19 | 13, 18 | syl5 28 | . . . 4 |
20 | 19 | exlimiv 1489 | . . 3 |
21 | 8, 20 | sylbi 114 | . 2 |
22 | 21 | impcom 116 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 wal 1241 wex 1381 wsb 1645 wmo 1901 |
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 |
This theorem depends on definitions: df-bi 110 df-nf 1350 df-sb 1646 df-eu 1903 df-mo 1904 |
This theorem is referenced by: eupick 1979 mopick2 1983 moexexdc 1984 euexex 1985 morex 2725 imadif 4979 funimaexglem 4982 |
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