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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 2306 |
. . 3
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2 | df-reu 2307 |
. . 3
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3 | 1, 2 | anbi12i 433 |
. 2
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4 | df-ral 2305 |
. . . . . . 7
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5 | ssel 2933 |
. . . . . . . . . . . . . 14
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6 | prth 326 |
. . . . . . . . . . . . . 14
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7 | 5, 6 | sylan 267 |
. . . . . . . . . . . . 13
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8 | 7 | exp4b 349 |
. . . . . . . . . . . 12
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9 | 8 | com23 72 |
. . . . . . . . . . 11
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10 | 9 | a2d 23 |
. . . . . . . . . 10
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11 | 10 | imp4a 331 |
. . . . . . . . 9
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12 | 11 | alimdv 1756 |
. . . . . . . 8
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13 | 12 | imp 115 |
. . . . . . 7
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14 | 4, 13 | sylan2b 271 |
. . . . . 6
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15 | euimmo 1964 |
. . . . . 6
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16 | 14, 15 | syl 14 |
. . . . 5
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17 | eu5 1944 |
. . . . . 6
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18 | 17 | simplbi2 367 |
. . . . 5
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19 | 16, 18 | syl9 66 |
. . . 4
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20 | 19 | imp32 244 |
. . 3
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21 | df-reu 2307 |
. . 3
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22 | 20, 21 | sylibr 137 |
. 2
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23 | 3, 22 | sylan2b 271 |
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 ax-ext 2019 |
This theorem depends on definitions: df-bi 110 df-nf 1347 df-sb 1643 df-eu 1900 df-mo 1901 df-clab 2024 df-cleq 2030 df-clel 2033 df-ral 2305 df-rex 2306 df-reu 2307 df-in 2918 df-ss 2925 |
This theorem is referenced by: reuss 3212 reuun1 3213 riotass2 5437 |
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