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Mirrors > Home > ILE Home > Th. List > reuss2 | Unicode version |
Description: Transfer uniqueness to a smaller subclass. (Contributed by NM, 20-Oct-2005.) |
Ref | Expression |
---|---|
reuss2 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-rex 2423 |
. . 3
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2 | df-reu 2424 |
. . 3
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3 | 1, 2 | anbi12i 456 |
. 2
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4 | df-ral 2422 |
. . . . . . 7
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5 | ssel 3096 |
. . . . . . . . . . . . . 14
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6 | anim12 342 |
. . . . . . . . . . . . . 14
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7 | 5, 6 | sylan 281 |
. . . . . . . . . . . . 13
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8 | 7 | exp4b 365 |
. . . . . . . . . . . 12
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9 | 8 | com23 78 |
. . . . . . . . . . 11
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10 | 9 | a2d 26 |
. . . . . . . . . 10
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11 | 10 | imp4a 347 |
. . . . . . . . 9
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12 | 11 | alimdv 1852 |
. . . . . . . 8
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13 | 12 | imp 123 |
. . . . . . 7
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14 | 4, 13 | sylan2b 285 |
. . . . . 6
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15 | euimmo 2067 |
. . . . . 6
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16 | 14, 15 | syl 14 |
. . . . 5
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17 | eu5 2047 |
. . . . . 6
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18 | 17 | simplbi2 383 |
. . . . 5
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19 | 16, 18 | syl9 72 |
. . . 4
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20 | 19 | imp32 255 |
. . 3
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21 | df-reu 2424 |
. . 3
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22 | 20, 21 | sylibr 133 |
. 2
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23 | 3, 22 | sylan2b 285 |
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 105 ax-ia2 106 ax-ia3 107 ax-io 699 ax-5 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-10 1484 ax-11 1485 ax-i12 1486 ax-bndl 1487 ax-4 1488 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 |
This theorem depends on definitions: df-bi 116 df-nf 1438 df-sb 1737 df-eu 2003 df-mo 2004 df-clab 2127 df-cleq 2133 df-clel 2136 df-ral 2422 df-rex 2423 df-reu 2424 df-in 3082 df-ss 3089 |
This theorem is referenced by: reuss 3362 reuun1 3363 riotass2 5764 |
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