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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 1506 | . . . 4 | |
2 | hbs1 1911 | . . . . 5 | |
3 | hbs1 1911 | . . . . 5 | |
4 | 2, 3 | hban 1526 | . . . 4 |
5 | sbequ12 1744 | . . . . 5 | |
6 | sbequ12 1744 | . . . . 5 | |
7 | 5, 6 | anbi12d 464 | . . . 4 |
8 | 1, 4, 7 | cbvexh 1728 | . . 3 |
9 | ax-17 1506 | . . . . . . 7 | |
10 | 9 | mo3h 2052 | . . . . . 6 |
11 | ax-4 1487 | . . . . . . 7 | |
12 | 11 | sps 1517 | . . . . . 6 |
13 | 10, 12 | sylbi 120 | . . . . 5 |
14 | sbequ2 1742 | . . . . . . . . 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 1577 | . . 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 1329 wex 1468 wsb 1735 wmo 2000 |
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 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 |
This theorem depends on definitions: df-bi 116 df-nf 1437 df-sb 1736 df-eu 2002 df-mo 2003 |
This theorem is referenced by: eupick 2078 mopick2 2082 moexexdc 2083 euexex 2084 morex 2868 imadif 5203 funimaexglem 5206 |
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