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Mirrors > Home > ILE Home > Th. List > euxfrdc | Unicode version |
Description: Transfer existential uniqueness from a variable to another variable contained in expression . (Contributed by NM, 14-Nov-2004.) |
Ref | Expression |
---|---|
euxfrdc.1 | |
euxfrdc.2 | |
euxfrdc.3 |
Ref | Expression |
---|---|
euxfrdc | DECID |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | euxfrdc.2 | . . . . . 6 | |
2 | euex 1930 | . . . . . 6 | |
3 | 1, 2 | ax-mp 7 | . . . . 5 |
4 | 3 | biantrur 287 | . . . 4 |
5 | 19.41v 1782 | . . . 4 | |
6 | euxfrdc.3 | . . . . . 6 | |
7 | 6 | pm5.32i 427 | . . . . 5 |
8 | 7 | exbii 1496 | . . . 4 |
9 | 4, 5, 8 | 3bitr2i 197 | . . 3 |
10 | 9 | eubii 1909 | . 2 |
11 | euxfrdc.1 | . . 3 | |
12 | 1 | eumoi 1933 | . . 3 |
13 | 11, 12 | euxfr2dc 2726 | . 2 DECID |
14 | 10, 13 | syl5bb 181 | 1 DECID |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 wb 98 DECID wdc 742 wceq 1243 wex 1381 wcel 1393 weu 1900 cvv 2557 |
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-dc 743 df-tru 1246 df-nf 1350 df-sb 1646 df-eu 1903 df-mo 1904 df-clab 2027 df-cleq 2033 df-clel 2036 df-v 2559 |
This theorem is referenced by: (None) |
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