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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 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax-17 1416 |
. . . 4
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2 | hbs1 1811 |
. . . . 5
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3 | hbs1 1811 |
. . . . 5
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4 | 2, 3 | hban 1436 |
. . . 4
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5 | sbequ12 1651 |
. . . . 5
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6 | sbequ12 1651 |
. . . . 5
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7 | 5, 6 | anbi12d 442 |
. . . 4
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8 | 1, 4, 7 | cbvexh 1635 |
. . 3
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9 | ax-17 1416 |
. . . . . . 7
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10 | 9 | mo3h 1950 |
. . . . . 6
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11 | ax-4 1397 |
. . . . . . 7
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12 | 11 | sps 1427 |
. . . . . 6
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13 | 10, 12 | sylbi 114 |
. . . . 5
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14 | sbequ2 1649 |
. . . . . . . . 9
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15 | 14 | imim2i 12 |
. . . . . . . 8
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16 | 15 | expd 245 |
. . . . . . 7
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17 | 16 | com4t 79 |
. . . . . 6
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18 | 17 | imp 115 |
. . . . 5
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19 | 13, 18 | syl5 28 |
. . . 4
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20 | 19 | exlimiv 1486 |
. . 3
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21 | 8, 20 | sylbi 114 |
. 2
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22 | 21 | impcom 116 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() |
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 629 ax-5 1333 ax-7 1334 ax-gen 1335 ax-ie1 1379 ax-ie2 1380 ax-8 1392 ax-10 1393 ax-11 1394 ax-i12 1395 ax-bndl 1396 ax-4 1397 ax-17 1416 ax-i9 1420 ax-ial 1424 ax-i5r 1425 |
This theorem depends on definitions: df-bi 110 df-nf 1347 df-sb 1643 df-eu 1900 df-mo 1901 |
This theorem is referenced by: eupick 1976 mopick2 1980 moexexdc 1981 euexex 1982 morex 2719 imadif 4922 funimaexglem 4925 |
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