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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 1509 | . . . . 5 | |
3 | 1, 2 | nfim 1552 | . . . 4 |
4 | 3 | nfal 1556 | . . 3 |
5 | nfv 1509 | . . 3 | |
6 | equequ2 1690 | . . . . 5 | |
7 | 6 | imbi2d 229 | . . . 4 |
8 | 7 | albidv 1797 | . . 3 |
9 | 4, 5, 8 | cbvex 1730 | . 2 |
10 | nfs1v 1913 | . . . . . . . 8 | |
11 | nfv 1509 | . . . . . . . 8 | |
12 | 10, 11 | nfim 1552 | . . . . . . 7 |
13 | sbequ2 1743 | . . . . . . . 8 | |
14 | ax-8 1483 | . . . . . . . 8 | |
15 | 13, 14 | imim12d 74 | . . . . . . 7 |
16 | 3, 12, 15 | cbv3 1721 | . . . . . 6 |
17 | 16 | ancli 321 | . . . . 5 |
18 | 3 | nfri 1500 | . . . . . 6 |
19 | 12 | nfri 1500 | . . . . . 6 |
20 | 18, 19 | aaanh 1566 | . . . . 5 |
21 | 17, 20 | sylibr 133 | . . . 4 |
22 | anim12 342 | . . . . . 6 | |
23 | equtr2 1688 | . . . . . 6 | |
24 | 22, 23 | syl6 33 | . . . . 5 |
25 | 24 | 2alimi 1433 | . . . 4 |
26 | 21, 25 | syl 14 | . . 3 |
27 | 26 | exlimiv 1578 | . 2 |
28 | 9, 27 | sylbir 134 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wal 1330 wnf 1437 wex 1469 wsb 1736 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-5 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-11 1485 ax-4 1488 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 |
This theorem depends on definitions: df-bi 116 df-nf 1438 df-sb 1737 |
This theorem is referenced by: modc 2043 eu2 2044 eu3h 2045 |
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