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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 1513 | . . . 4 | |
2 | hbs1 1925 | . . . . 5 | |
3 | hbs1 1925 | . . . . 5 | |
4 | 2, 3 | hban 1534 | . . . 4 |
5 | sbequ12 1758 | . . . . 5 | |
6 | sbequ12 1758 | . . . . 5 | |
7 | 5, 6 | anbi12d 465 | . . . 4 |
8 | 1, 4, 7 | cbvexh 1742 | . . 3 |
9 | ax-17 1513 | . . . . . . 7 | |
10 | 9 | mo3h 2066 | . . . . . 6 |
11 | ax-4 1497 | . . . . . . 7 | |
12 | 11 | sps 1524 | . . . . . 6 |
13 | 10, 12 | sylbi 120 | . . . . 5 |
14 | sbequ2 1756 | . . . . . . . . 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 1585 | . . 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 1340 wex 1479 wsb 1749 wmo 2014 |
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 699 ax-5 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-10 1492 ax-11 1493 ax-i12 1494 ax-bndl 1496 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 |
This theorem depends on definitions: df-bi 116 df-nf 1448 df-sb 1750 df-eu 2016 df-mo 2017 |
This theorem is referenced by: eupick 2092 mopick2 2096 moexexdc 2097 euexex 2098 morex 2908 imadif 5265 funimaexglem 5268 |
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