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Mirrors > Home > ILE Home > Th. List > euexex | Unicode version |
Description: Existential uniqueness and "at most one" double quantification. (Contributed by Jim Kingdon, 28-Dec-2018.) |
Ref | Expression |
---|---|
euexex.1 |
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Ref | Expression |
---|---|
euexex |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eu5 1944 |
. . 3
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2 | nfmo1 1909 |
. . . . . 6
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3 | nfa1 1431 |
. . . . . . 7
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4 | nfe1 1382 |
. . . . . . . 8
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5 | 4 | nfmo 1917 |
. . . . . . 7
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6 | 3, 5 | nfim 1461 |
. . . . . 6
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7 | 2, 6 | nfim 1461 |
. . . . 5
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8 | euexex.1 |
. . . . . . 7
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9 | 8 | nfmo 1917 |
. . . . . . 7
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10 | mopick 1975 |
. . . . . . . . 9
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11 | 10 | ex 108 |
. . . . . . . 8
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12 | 11 | com3r 73 |
. . . . . . 7
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13 | 8, 9, 12 | alrimd 1498 |
. . . . . 6
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14 | moim 1961 |
. . . . . . 7
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15 | 14 | spsd 1428 |
. . . . . 6
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16 | 13, 15 | syl6 29 |
. . . . 5
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17 | 7, 16 | exlimi 1482 |
. . . 4
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18 | 17 | imp 115 |
. . 3
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19 | 1, 18 | sylbi 114 |
. 2
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20 | 19 | imp 115 |
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-tru 1245 df-nf 1347 df-sb 1643 df-eu 1900 df-mo 1901 |
This theorem is referenced by: mosubt 2712 funco 4883 |
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