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Mirrors > Home > ILE Home > Th. List > mo23 | Unicode version |
Description: An implication between two definitions of "there exists at most one." (Contributed by Jim Kingdon, 25-Jun-2018.) |
Ref | Expression |
---|---|
mo23.1 |
Ref | Expression |
---|---|
mo23 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | mo23.1 | . . . . 5 | |
2 | nfv 1421 | . . . . 5 | |
3 | 1, 2 | nfim 1464 | . . . 4 |
4 | 3 | nfal 1468 | . . 3 |
5 | nfv 1421 | . . 3 | |
6 | equequ2 1599 | . . . . 5 | |
7 | 6 | imbi2d 219 | . . . 4 |
8 | 7 | albidv 1705 | . . 3 |
9 | 4, 5, 8 | cbvex 1639 | . 2 |
10 | nfs1v 1815 | . . . . . . . 8 | |
11 | nfv 1421 | . . . . . . . 8 | |
12 | 10, 11 | nfim 1464 | . . . . . . 7 |
13 | sbequ2 1652 | . . . . . . . 8 | |
14 | ax-8 1395 | . . . . . . . 8 | |
15 | 13, 14 | imim12d 68 | . . . . . . 7 |
16 | 3, 12, 15 | cbv3 1630 | . . . . . 6 |
17 | 16 | ancli 306 | . . . . 5 |
18 | 3 | nfri 1412 | . . . . . 6 |
19 | 12 | nfri 1412 | . . . . . 6 |
20 | 18, 19 | aaanh 1478 | . . . . 5 |
21 | 17, 20 | sylibr 137 | . . . 4 |
22 | prth 326 | . . . . . 6 | |
23 | equtr2 1597 | . . . . . 6 | |
24 | 22, 23 | syl6 29 | . . . . 5 |
25 | 24 | 2alimi 1345 | . . . 4 |
26 | 21, 25 | syl 14 | . . 3 |
27 | 26 | exlimiv 1489 | . 2 |
28 | 9, 27 | sylbir 125 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 wal 1241 wnf 1349 wex 1381 wsb 1645 |
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-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-11 1397 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 |
This theorem is referenced by: modc 1943 eu2 1944 eu3h 1945 |
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