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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 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-rex 2354 | . . 3 | |
2 | df-reu 2355 | . . 3 | |
3 | 1, 2 | anbi12i 447 | . 2 |
4 | df-ral 2353 | . . . . . . 7 | |
5 | ssel 2993 | . . . . . . . . . . . . . 14 | |
6 | prth 336 | . . . . . . . . . . . . . 14 | |
7 | 5, 6 | sylan 277 | . . . . . . . . . . . . 13 |
8 | 7 | exp4b 359 | . . . . . . . . . . . 12 |
9 | 8 | com23 77 | . . . . . . . . . . 11 |
10 | 9 | a2d 26 | . . . . . . . . . 10 |
11 | 10 | imp4a 341 | . . . . . . . . 9 |
12 | 11 | alimdv 1800 | . . . . . . . 8 |
13 | 12 | imp 122 | . . . . . . 7 |
14 | 4, 13 | sylan2b 281 | . . . . . 6 |
15 | euimmo 2008 | . . . . . 6 | |
16 | 14, 15 | syl 14 | . . . . 5 |
17 | eu5 1988 | . . . . . 6 | |
18 | 17 | simplbi2 377 | . . . . 5 |
19 | 16, 18 | syl9 71 | . . . 4 |
20 | 19 | imp32 253 | . . 3 |
21 | df-reu 2355 | . . 3 | |
22 | 20, 21 | sylibr 132 | . 2 |
23 | 3, 22 | sylan2b 281 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 102 wal 1282 wex 1421 wcel 1433 weu 1941 wmo 1942 wral 2348 wrex 2349 wreu 2350 wss 2973 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-io 662 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-10 1436 ax-11 1437 ax-i12 1438 ax-bndl 1439 ax-4 1440 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 |
This theorem depends on definitions: df-bi 115 df-nf 1390 df-sb 1686 df-eu 1944 df-mo 1945 df-clab 2068 df-cleq 2074 df-clel 2077 df-ral 2353 df-rex 2354 df-reu 2355 df-in 2979 df-ss 2986 |
This theorem is referenced by: reuss 3245 reuun1 3246 riotass2 5514 |
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