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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 1515 | . . . . 5 | |
3 | 1, 2 | nfim 1559 | . . . 4 |
4 | 3 | nfal 1563 | . . 3 |
5 | nfv 1515 | . . 3 | |
6 | equequ2 1700 | . . . . 5 | |
7 | 6 | imbi2d 229 | . . . 4 |
8 | 7 | albidv 1811 | . . 3 |
9 | 4, 5, 8 | cbvex 1743 | . 2 |
10 | nfs1v 1926 | . . . . . . . 8 | |
11 | nfv 1515 | . . . . . . . 8 | |
12 | 10, 11 | nfim 1559 | . . . . . . 7 |
13 | sbequ2 1756 | . . . . . . . 8 | |
14 | ax-8 1491 | . . . . . . . 8 | |
15 | 13, 14 | imim12d 74 | . . . . . . 7 |
16 | 3, 12, 15 | cbv3 1729 | . . . . . 6 |
17 | 16 | ancli 321 | . . . . 5 |
18 | 3 | nfri 1506 | . . . . . 6 |
19 | 12 | nfri 1506 | . . . . . 6 |
20 | 18, 19 | aaanh 1573 | . . . . 5 |
21 | 17, 20 | sylibr 133 | . . . 4 |
22 | anim12 342 | . . . . . 6 | |
23 | equtr2 1698 | . . . . . 6 | |
24 | 22, 23 | syl6 33 | . . . . 5 |
25 | 24 | 2alimi 1443 | . . . 4 |
26 | 21, 25 | syl 14 | . . 3 |
27 | 26 | exlimiv 1585 | . 2 |
28 | 9, 27 | sylbir 134 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wal 1340 wnf 1447 wex 1479 wsb 1749 |
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 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-11 1493 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 |
This theorem depends on definitions: df-bi 116 df-nf 1448 df-sb 1750 |
This theorem is referenced by: modc 2056 eu2 2057 eu3h 2058 |
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