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Mirrors > Home > ILE Home > Th. List > eusv2nf | Unicode version |
Description: Two ways to express single-valuedness of a class expression . (Contributed by Mario Carneiro, 18-Nov-2016.) |
Ref | Expression |
---|---|
eusv2.1 |
Ref | Expression |
---|---|
eusv2nf |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfeu1 1911 | . . . 4 | |
2 | nfe1 1385 | . . . . . . 7 | |
3 | 2 | nfeu 1919 | . . . . . 6 |
4 | eusv2.1 | . . . . . . . . 9 | |
5 | 4 | isseti 2563 | . . . . . . . 8 |
6 | 19.8a 1482 | . . . . . . . . 9 | |
7 | 6 | ancri 307 | . . . . . . . 8 |
8 | 5, 7 | eximii 1493 | . . . . . . 7 |
9 | eupick 1979 | . . . . . . 7 | |
10 | 8, 9 | mpan2 401 | . . . . . 6 |
11 | 3, 10 | alrimi 1415 | . . . . 5 |
12 | nf3 1559 | . . . . 5 | |
13 | 11, 12 | sylibr 137 | . . . 4 |
14 | 1, 13 | alrimi 1415 | . . 3 |
15 | dfnfc2 3598 | . . . 4 | |
16 | 15, 4 | mpg 1340 | . . 3 |
17 | 14, 16 | sylibr 137 | . 2 |
18 | eusvnfb 4186 | . . . 4 | |
19 | 4, 18 | mpbiran2 848 | . . 3 |
20 | eusv2i 4187 | . . 3 | |
21 | 19, 20 | sylbir 125 | . 2 |
22 | 17, 21 | impbii 117 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 wb 98 wal 1241 wceq 1243 wnf 1349 wex 1381 wcel 1393 weu 1900 wnfc 2165 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-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-nf 1350 df-sb 1646 df-eu 1903 df-mo 1904 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-rex 2312 df-v 2559 df-sbc 2765 df-csb 2853 df-un 2922 df-sn 3381 df-pr 3382 df-uni 3581 |
This theorem is referenced by: eusv2 4189 |
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