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Mirrors > Home > ILE Home > Th. List > eu2 | Unicode version |
Description: An alternate way of defining existential uniqueness. Definition 6.10 of [TakeutiZaring] p. 26. (Contributed by NM, 8-Jul-1994.) |
Ref | Expression |
---|---|
eu2.1 |
Ref | Expression |
---|---|
eu2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | euex 1930 | . . 3 | |
2 | eu2.1 | . . . . . 6 | |
3 | 2 | nfri 1412 | . . . . 5 |
4 | 3 | eumo0 1931 | . . . 4 |
5 | 2 | mo23 1941 | . . . 4 |
6 | 4, 5 | syl 14 | . . 3 |
7 | 1, 6 | jca 290 | . 2 |
8 | 19.29r 1512 | . . . 4 | |
9 | impexp 250 | . . . . . . . . 9 | |
10 | 9 | albii 1359 | . . . . . . . 8 |
11 | 2 | 19.21 1475 | . . . . . . . 8 |
12 | 10, 11 | bitri 173 | . . . . . . 7 |
13 | 12 | anbi2i 430 | . . . . . 6 |
14 | abai 494 | . . . . . 6 | |
15 | 13, 14 | bitr4i 176 | . . . . 5 |
16 | 15 | exbii 1496 | . . . 4 |
17 | 8, 16 | sylib 127 | . . 3 |
18 | 3 | eu1 1925 | . . 3 |
19 | 17, 18 | sylibr 137 | . 2 |
20 | 7, 19 | impbii 117 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 wb 98 wal 1241 wnf 1349 wex 1381 wsb 1645 weu 1900 |
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 |
This theorem depends on definitions: df-bi 110 df-nf 1350 df-sb 1646 df-eu 1903 |
This theorem is referenced by: eu3h 1945 mo3h 1953 bm1.1 2025 reu2 2729 |
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