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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 1971 | . . 3 | |
2 | eu2.1 | . . . . . 6 | |
3 | 2 | nfri 1452 | . . . . 5 |
4 | 3 | eumo0 1972 | . . . 4 |
5 | 2 | mo23 1982 | . . . 4 |
6 | 4, 5 | syl 14 | . . 3 |
7 | 1, 6 | jca 300 | . 2 |
8 | 19.29r 1552 | . . . 4 | |
9 | impexp 259 | . . . . . . . . 9 | |
10 | 9 | albii 1399 | . . . . . . . 8 |
11 | 2 | 19.21 1515 | . . . . . . . 8 |
12 | 10, 11 | bitri 182 | . . . . . . 7 |
13 | 12 | anbi2i 444 | . . . . . 6 |
14 | abai 524 | . . . . . 6 | |
15 | 13, 14 | bitr4i 185 | . . . . 5 |
16 | 15 | exbii 1536 | . . . 4 |
17 | 8, 16 | sylib 120 | . . 3 |
18 | 3 | eu1 1966 | . . 3 |
19 | 17, 18 | sylibr 132 | . 2 |
20 | 7, 19 | impbii 124 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 102 wb 103 wal 1282 wnf 1389 wex 1421 wsb 1685 weu 1941 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-io 662 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-10 1436 ax-11 1437 ax-i12 1438 ax-bndl 1439 ax-4 1440 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 |
This theorem depends on definitions: df-bi 115 df-nf 1390 df-sb 1686 df-eu 1944 |
This theorem is referenced by: eu3h 1986 mo3h 1994 bm1.1 2066 reu2 2780 |
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