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Mirrors > Home > ILE Home > Th. List > moexexdc | Unicode version |
Description: "At most one" double quantification. (Contributed by Jim Kingdon, 5-Jul-2018.) |
Ref | Expression |
---|---|
moexexdc.1 |
Ref | Expression |
---|---|
moexexdc | DECID |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-dc 743 | . 2 DECID | |
2 | hbmo1 1938 | . . . . . 6 | |
3 | hba1 1433 | . . . . . . 7 | |
4 | hbe1 1384 | . . . . . . . 8 | |
5 | 4 | hbmo 1939 | . . . . . . 7 |
6 | 3, 5 | hbim 1437 | . . . . . 6 |
7 | 2, 6 | hbim 1437 | . . . . 5 |
8 | moexexdc.1 | . . . . . . . 8 | |
9 | 8 | nfri 1412 | . . . . . . 7 |
10 | 9 | hbmo 1939 | . . . . . . 7 |
11 | mopick 1978 | . . . . . . . . 9 | |
12 | 11 | ex 108 | . . . . . . . 8 |
13 | 12 | com3r 73 | . . . . . . 7 |
14 | 9, 10, 13 | alrimdh 1368 | . . . . . 6 |
15 | moim 1964 | . . . . . . 7 | |
16 | 15 | spsd 1431 | . . . . . 6 |
17 | 14, 16 | syl6 29 | . . . . 5 |
18 | 7, 17 | exlimih 1484 | . . . 4 |
19 | 9 | hbex 1527 | . . . . . . . . 9 |
20 | exsimpl 1508 | . . . . . . . . 9 | |
21 | 19, 20 | exlimih 1484 | . . . . . . . 8 |
22 | 21 | con3i 562 | . . . . . . 7 |
23 | mon 1929 | . . . . . . 7 | |
24 | 22, 23 | syl 14 | . . . . . 6 |
25 | 24 | a1d 22 | . . . . 5 |
26 | 25 | a1d 22 | . . . 4 |
27 | 18, 26 | jaoi 636 | . . 3 |
28 | 27 | impd 242 | . 2 |
29 | 1, 28 | sylbi 114 | 1 DECID |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wa 97 wo 629 DECID wdc 742 wal 1241 wnf 1349 wex 1381 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-in1 544 ax-in2 545 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-dc 743 df-tru 1246 df-nf 1350 df-sb 1646 df-eu 1903 df-mo 1904 |
This theorem is referenced by: 2moswapdc 1990 |
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