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Mirrors > Home > ILE Home > Th. List > 2rmorex | Unicode version |
Description: Double restricted quantification with "at most one," analogous to 2moex 1986. (Contributed by Alexander van der Vekens, 17-Jun-2017.) |
Ref | Expression |
---|---|
2rmorex |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-rex 2312 | . . . . . . . 8 | |
2 | 1 | anbi2i 430 | . . . . . . 7 |
3 | 2 | mobii 1937 | . . . . . 6 |
4 | df-rmo 2314 | . . . . . 6 | |
5 | 19.42v 1786 | . . . . . . 7 | |
6 | 5 | mobii 1937 | . . . . . 6 |
7 | 3, 4, 6 | 3bitr4i 201 | . . . . 5 |
8 | 2moex 1986 | . . . . 5 | |
9 | 7, 8 | sylbi 114 | . . . 4 |
10 | an12 495 | . . . . . 6 | |
11 | 10 | mobii 1937 | . . . . 5 |
12 | 11 | albii 1359 | . . . 4 |
13 | 9, 12 | sylib 127 | . . 3 |
14 | moanimv 1975 | . . . 4 | |
15 | 14 | albii 1359 | . . 3 |
16 | 13, 15 | sylib 127 | . 2 |
17 | df-ral 2311 | . . 3 | |
18 | df-rmo 2314 | . . . . 5 | |
19 | 18 | imbi2i 215 | . . . 4 |
20 | 19 | albii 1359 | . . 3 |
21 | 17, 20 | bitri 173 | . 2 |
22 | 16, 21 | sylibr 137 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 wal 1241 wex 1381 wcel 1393 wmo 1901 wral 2306 wrex 2307 wrmo 2309 |
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-tru 1246 df-nf 1350 df-sb 1646 df-eu 1903 df-mo 1904 df-ral 2311 df-rex 2312 df-rmo 2314 |
This theorem is referenced by: (None) |
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