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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 585 | . . . . 5 | |
2 | 1 | imbi1i 237 | . . . 4 |
3 | impexp 261 | . . . 4 | |
4 | sban 1948 | . . . . . . 7 | |
5 | moanim.1 | . . . . . . . . 9 | |
6 | 5 | sbf 1770 | . . . . . . . 8 |
7 | 6 | anbi1i 455 | . . . . . . 7 |
8 | 4, 7 | bitr2i 184 | . . . . . 6 |
9 | 8 | anbi2i 454 | . . . . 5 |
10 | 9 | imbi1i 237 | . . . 4 |
11 | 2, 3, 10 | 3bitr3i 209 | . . 3 |
12 | 11 | 2albii 1464 | . 2 |
13 | 5 | 19.21 1576 | . . 3 |
14 | 19.21v 1866 | . . . 4 | |
15 | 14 | albii 1463 | . . 3 |
16 | ax-17 1519 | . . . . 5 | |
17 | 16 | mo3h 2072 | . . . 4 |
18 | 17 | imbi2i 225 | . . 3 |
19 | 13, 15, 18 | 3bitr4ri 212 | . 2 |
20 | ax-17 1519 | . . 3 | |
21 | 20 | mo3h 2072 | . 2 |
22 | 12, 19, 21 | 3bitr4ri 212 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wal 1346 wnf 1453 wsb 1755 wmo 2020 |
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-io 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 |
This theorem depends on definitions: df-bi 116 df-nf 1454 df-sb 1756 df-eu 2022 df-mo 2023 |
This theorem is referenced by: moanimv 2094 moaneu 2095 moanmo 2096 |
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