Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > reuun2 | Unicode version |
Description: Transfer uniqueness to a smaller or larger class. (Contributed by NM, 21-Oct-2005.) |
Ref | Expression |
---|---|
reuun2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-rex 2312 | . . 3 | |
2 | euor2 1958 | . . 3 | |
3 | 1, 2 | sylnbi 603 | . 2 |
4 | df-reu 2313 | . . 3 | |
5 | elun 3084 | . . . . . 6 | |
6 | 5 | anbi1i 431 | . . . . 5 |
7 | andir 732 | . . . . . 6 | |
8 | orcom 647 | . . . . . 6 | |
9 | 7, 8 | bitri 173 | . . . . 5 |
10 | 6, 9 | bitri 173 | . . . 4 |
11 | 10 | eubii 1909 | . . 3 |
12 | 4, 11 | bitri 173 | . 2 |
13 | df-reu 2313 | . 2 | |
14 | 3, 12, 13 | 3bitr4g 212 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wa 97 wb 98 wo 629 wex 1381 wcel 1393 weu 1900 wrex 2307 wreu 2308 cun 2915 |
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-in1 544 ax-in2 545 ax-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 |
This theorem depends on definitions: df-bi 110 df-tru 1246 df-fal 1249 df-nf 1350 df-sb 1646 df-eu 1903 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-rex 2312 df-reu 2313 df-v 2559 df-un 2922 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |