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Mirrors > Home > ILE Home > Th. List > mo23 | Unicode version |
Description: An implication between two definitions of "there exists at most one." (Contributed by Jim Kingdon, 25-Jun-2018.) |
Ref | Expression |
---|---|
mo23.1 |
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Ref | Expression |
---|---|
mo23 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | mo23.1 |
. . . . 5
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2 | nfv 1418 |
. . . . 5
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3 | 1, 2 | nfim 1461 |
. . . 4
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4 | 3 | nfal 1465 |
. . 3
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5 | nfv 1418 |
. . 3
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6 | equequ2 1596 |
. . . . 5
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7 | 6 | imbi2d 219 |
. . . 4
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8 | 7 | albidv 1702 |
. . 3
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9 | 4, 5, 8 | cbvex 1636 |
. 2
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10 | nfs1v 1812 |
. . . . . . . 8
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11 | nfv 1418 |
. . . . . . . 8
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12 | 10, 11 | nfim 1461 |
. . . . . . 7
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13 | sbequ2 1649 |
. . . . . . . 8
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14 | ax-8 1392 |
. . . . . . . 8
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15 | 13, 14 | imim12d 68 |
. . . . . . 7
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16 | 3, 12, 15 | cbv3 1627 |
. . . . . 6
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17 | 16 | ancli 306 |
. . . . 5
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18 | 3 | nfri 1409 |
. . . . . 6
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19 | 12 | nfri 1409 |
. . . . . 6
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20 | 18, 19 | aaanh 1475 |
. . . . 5
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21 | 17, 20 | sylibr 137 |
. . . 4
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22 | prth 326 |
. . . . . 6
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23 | equtr2 1594 |
. . . . . 6
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24 | 22, 23 | syl6 29 |
. . . . 5
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25 | 24 | 2alimi 1342 |
. . . 4
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26 | 21, 25 | syl 14 |
. . 3
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27 | 26 | exlimiv 1486 |
. 2
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28 | 9, 27 | sylbir 125 |
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-5 1333 ax-7 1334 ax-gen 1335 ax-ie1 1379 ax-ie2 1380 ax-8 1392 ax-11 1394 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 |
This theorem is referenced by: modc 1940 eu2 1941 eu3h 1942 |
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