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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 2376 |
. . 3
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2 | df-reu 2377 |
. . 3
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3 | 1, 2 | anbi12i 449 |
. 2
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4 | df-ral 2375 |
. . . . . . 7
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5 | ssel 3033 |
. . . . . . . . . . . . . 14
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6 | prth 337 |
. . . . . . . . . . . . . 14
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7 | 5, 6 | sylan 278 |
. . . . . . . . . . . . 13
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8 | 7 | exp4b 360 |
. . . . . . . . . . . 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 342 |
. . . . . . . . 9
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12 | 11 | alimdv 1814 |
. . . . . . . 8
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13 | 12 | imp 123 |
. . . . . . 7
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14 | 4, 13 | sylan2b 282 |
. . . . . 6
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15 | euimmo 2022 |
. . . . . 6
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16 | 14, 15 | syl 14 |
. . . . 5
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17 | eu5 2002 |
. . . . . 6
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18 | 17 | simplbi2 378 |
. . . . 5
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19 | 16, 18 | syl9 72 |
. . . 4
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20 | 19 | imp32 254 |
. . 3
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21 | df-reu 2377 |
. . 3
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22 | 20, 21 | sylibr 133 |
. 2
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23 | 3, 22 | sylan2b 282 |
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 105 ax-ia2 106 ax-ia3 107 ax-io 668 ax-5 1388 ax-7 1389 ax-gen 1390 ax-ie1 1434 ax-ie2 1435 ax-8 1447 ax-10 1448 ax-11 1449 ax-i12 1450 ax-bndl 1451 ax-4 1452 ax-17 1471 ax-i9 1475 ax-ial 1479 ax-i5r 1480 ax-ext 2077 |
This theorem depends on definitions: df-bi 116 df-nf 1402 df-sb 1700 df-eu 1958 df-mo 1959 df-clab 2082 df-cleq 2088 df-clel 2091 df-ral 2375 df-rex 2376 df-reu 2377 df-in 3019 df-ss 3026 |
This theorem is referenced by: reuss 3296 reuun1 3297 riotass2 5672 |
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