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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 2420 | . . 3 | |
2 | df-reu 2421 | . . 3 | |
3 | 1, 2 | anbi12i 455 | . 2 |
4 | df-ral 2419 | . . . . . . 7 | |
5 | ssel 3086 | . . . . . . . . . . . . . 14 | |
6 | anim12 341 | . . . . . . . . . . . . . 14 | |
7 | 5, 6 | sylan 281 | . . . . . . . . . . . . 13 |
8 | 7 | exp4b 364 | . . . . . . . . . . . 12 |
9 | 8 | com23 78 | . . . . . . . . . . 11 |
10 | 9 | a2d 26 | . . . . . . . . . 10 |
11 | 10 | imp4a 346 | . . . . . . . . 9 |
12 | 11 | alimdv 1851 | . . . . . . . 8 |
13 | 12 | imp 123 | . . . . . . 7 |
14 | 4, 13 | sylan2b 285 | . . . . . 6 |
15 | euimmo 2064 | . . . . . 6 | |
16 | 14, 15 | syl 14 | . . . . 5 |
17 | eu5 2044 | . . . . . 6 | |
18 | 17 | simplbi2 382 | . . . . 5 |
19 | 16, 18 | syl9 72 | . . . 4 |
20 | 19 | imp32 255 | . . 3 |
21 | df-reu 2421 | . . 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 1329 wex 1468 wcel 1480 weu 1997 wmo 1998 wral 2414 wrex 2415 wreu 2416 wss 3066 |
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 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2119 |
This theorem depends on definitions: df-bi 116 df-nf 1437 df-sb 1736 df-eu 2000 df-mo 2001 df-clab 2124 df-cleq 2130 df-clel 2133 df-ral 2419 df-rex 2420 df-reu 2421 df-in 3072 df-ss 3079 |
This theorem is referenced by: reuss 3352 reuun1 3353 riotass2 5749 |
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