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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 1491 | . . . 4 | |
2 | hbs1 1891 | . . . . 5 | |
3 | hbs1 1891 | . . . . 5 | |
4 | 2, 3 | hban 1511 | . . . 4 |
5 | sbequ12 1729 | . . . . 5 | |
6 | sbequ12 1729 | . . . . 5 | |
7 | 5, 6 | anbi12d 464 | . . . 4 |
8 | 1, 4, 7 | cbvexh 1713 | . . 3 |
9 | ax-17 1491 | . . . . . . 7 | |
10 | 9 | mo3h 2030 | . . . . . 6 |
11 | ax-4 1472 | . . . . . . 7 | |
12 | 11 | sps 1502 | . . . . . 6 |
13 | 10, 12 | sylbi 120 | . . . . 5 |
14 | sbequ2 1727 | . . . . . . . . 9 | |
15 | 14 | imim2i 12 | . . . . . . . 8 |
16 | 15 | expd 256 | . . . . . . 7 |
17 | 16 | com4t 85 | . . . . . 6 |
18 | 17 | imp 123 | . . . . 5 |
19 | 13, 18 | syl5 32 | . . . 4 |
20 | 19 | exlimiv 1562 | . . 3 |
21 | 8, 20 | sylbi 120 | . 2 |
22 | 21 | impcom 124 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wal 1314 wex 1453 wsb 1720 wmo 1978 |
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 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 |
This theorem depends on definitions: df-bi 116 df-nf 1422 df-sb 1721 df-eu 1980 df-mo 1981 |
This theorem is referenced by: eupick 2056 mopick2 2060 moexexdc 2061 euexex 2062 morex 2841 imadif 5173 funimaexglem 5176 |
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