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Mirrors > Home > ILE Home > Th. List > moanim | Unicode version |
Description: Introduction of a conjunct into "at most one" quantifier. (Contributed by NM, 3-Dec-2001.) |
Ref | Expression |
---|---|
moanim.1 |
Ref | Expression |
---|---|
moanim |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | anandi 524 | . . . . 5 | |
2 | 1 | imbi1i 227 | . . . 4 |
3 | impexp 250 | . . . 4 | |
4 | sban 1829 | . . . . . . 7 | |
5 | moanim.1 | . . . . . . . . 9 | |
6 | 5 | sbf 1660 | . . . . . . . 8 |
7 | 6 | anbi1i 431 | . . . . . . 7 |
8 | 4, 7 | bitr2i 174 | . . . . . 6 |
9 | 8 | anbi2i 430 | . . . . 5 |
10 | 9 | imbi1i 227 | . . . 4 |
11 | 2, 3, 10 | 3bitr3i 199 | . . 3 |
12 | 11 | 2albii 1360 | . 2 |
13 | 5 | 19.21 1475 | . . 3 |
14 | 19.21v 1753 | . . . 4 | |
15 | 14 | albii 1359 | . . 3 |
16 | ax-17 1419 | . . . . 5 | |
17 | 16 | mo3h 1953 | . . . 4 |
18 | 17 | imbi2i 215 | . . 3 |
19 | 13, 15, 18 | 3bitr4ri 202 | . 2 |
20 | ax-17 1419 | . . 3 | |
21 | 20 | mo3h 1953 | . 2 |
22 | 12, 19, 21 | 3bitr4ri 202 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 wb 98 wal 1241 wnf 1349 wsb 1645 wmo 1901 |
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 df-mo 1904 |
This theorem is referenced by: moanimv 1975 moaneu 1976 moanmo 1977 |
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