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Mirrors > Home > ILE Home > Th. List > reu3 | Unicode version |
Description: A way to express restricted uniqueness. (Contributed by NM, 24-Oct-2006.) |
Ref | Expression |
---|---|
reu3 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | reurex 2523 |
. . 3
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2 | reu6 2730 |
. . . 4
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3 | bi1 111 |
. . . . . 6
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4 | 3 | ralimi 2384 |
. . . . 5
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5 | 4 | reximi 2416 |
. . . 4
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6 | 2, 5 | sylbi 114 |
. . 3
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7 | 1, 6 | jca 290 |
. 2
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8 | rexex 2368 |
. . . 4
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9 | 8 | anim2i 324 |
. . 3
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10 | nfv 1421 |
. . . . 5
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11 | 10 | eu3 1946 |
. . . 4
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12 | df-reu 2313 |
. . . 4
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13 | df-rex 2312 |
. . . . 5
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14 | df-ral 2311 |
. . . . . . 7
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15 | impexp 250 |
. . . . . . . 8
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16 | 15 | albii 1359 |
. . . . . . 7
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17 | 14, 16 | bitr4i 176 |
. . . . . 6
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18 | 17 | exbii 1496 |
. . . . 5
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19 | 13, 18 | anbi12i 433 |
. . . 4
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20 | 11, 12, 19 | 3bitr4i 201 |
. . 3
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21 | 9, 20 | sylibr 137 |
. 2
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22 | 7, 21 | impbii 117 |
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 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 |
This theorem depends on definitions: df-bi 110 df-nf 1350 df-sb 1646 df-eu 1903 df-mo 1904 df-cleq 2033 df-clel 2036 df-ral 2311 df-rex 2312 df-reu 2313 df-rmo 2314 |
This theorem is referenced by: reu7 2736 bdreu 9975 |
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