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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 2691 |
. . 3
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2 | reu6 2928 |
. . . 4
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3 | biimp 118 |
. . . . . 6
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4 | 3 | ralimi 2540 |
. . . . 5
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5 | 4 | reximi 2574 |
. . . 4
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6 | 2, 5 | sylbi 121 |
. . 3
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7 | 1, 6 | jca 306 |
. 2
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8 | rexex 2523 |
. . . 4
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9 | 8 | anim2i 342 |
. . 3
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10 | nfv 1528 |
. . . . 5
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11 | 10 | eu3 2072 |
. . . 4
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12 | df-reu 2462 |
. . . 4
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13 | df-rex 2461 |
. . . . 5
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14 | df-ral 2460 |
. . . . . . 7
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15 | impexp 263 |
. . . . . . . 8
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16 | 15 | albii 1470 |
. . . . . . 7
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17 | 14, 16 | bitr4i 187 |
. . . . . 6
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18 | 17 | exbii 1605 |
. . . . 5
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19 | 13, 18 | anbi12i 460 |
. . . 4
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20 | 11, 12, 19 | 3bitr4i 212 |
. . 3
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21 | 9, 20 | sylibr 134 |
. 2
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22 | 7, 21 | impbii 126 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-io 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-ext 2159 |
This theorem depends on definitions: df-bi 117 df-nf 1461 df-sb 1763 df-eu 2029 df-mo 2030 df-cleq 2170 df-clel 2173 df-ral 2460 df-rex 2461 df-reu 2462 df-rmo 2463 |
This theorem is referenced by: reu7 2934 bdreu 14646 |
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