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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 2454 | . . 3 | |
2 | df-reu 2455 | . . 3 | |
3 | 1, 2 | anbi12i 457 | . 2 |
4 | df-ral 2453 | . . . . . . 7 | |
5 | ssel 3141 | . . . . . . . . . . . . . 14 | |
6 | anim12 342 | . . . . . . . . . . . . . 14 | |
7 | 5, 6 | sylan 281 | . . . . . . . . . . . . 13 |
8 | 7 | exp4b 365 | . . . . . . . . . . . 12 |
9 | 8 | com23 78 | . . . . . . . . . . 11 |
10 | 9 | a2d 26 | . . . . . . . . . 10 |
11 | 10 | imp4a 347 | . . . . . . . . 9 |
12 | 11 | alimdv 1872 | . . . . . . . 8 |
13 | 12 | imp 123 | . . . . . . 7 |
14 | 4, 13 | sylan2b 285 | . . . . . 6 |
15 | euimmo 2086 | . . . . . 6 | |
16 | 14, 15 | syl 14 | . . . . 5 |
17 | eu5 2066 | . . . . . 6 | |
18 | 17 | simplbi2 383 | . . . . 5 |
19 | 16, 18 | syl9 72 | . . . 4 |
20 | 19 | imp32 255 | . . 3 |
21 | df-reu 2455 | . . 3 | |
22 | 20, 21 | sylibr 133 | . 2 |
23 | 3, 22 | sylan2b 285 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wal 1346 wex 1485 weu 2019 wmo 2020 wcel 2141 wral 2448 wrex 2449 wreu 2450 wss 3121 |
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 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-ext 2152 |
This theorem depends on definitions: df-bi 116 df-nf 1454 df-sb 1756 df-eu 2022 df-mo 2023 df-clab 2157 df-cleq 2163 df-clel 2166 df-ral 2453 df-rex 2454 df-reu 2455 df-in 3127 df-ss 3134 |
This theorem is referenced by: reuss 3408 reuun1 3409 riotass2 5833 |
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