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Mirrors > Home > ILE Home > Th. List > 2rmorex | Unicode version |
Description: Double restricted quantification with "at most one," analogous to 2moex 2027. (Contributed by Alexander van der Vekens, 17-Jun-2017.) |
Ref | Expression |
---|---|
2rmorex |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-rex 2354 | . . . . . . . 8 | |
2 | 1 | anbi2i 444 | . . . . . . 7 |
3 | 2 | mobii 1978 | . . . . . 6 |
4 | df-rmo 2356 | . . . . . 6 | |
5 | 19.42v 1827 | . . . . . . 7 | |
6 | 5 | mobii 1978 | . . . . . 6 |
7 | 3, 4, 6 | 3bitr4i 210 | . . . . 5 |
8 | 2moex 2027 | . . . . 5 | |
9 | 7, 8 | sylbi 119 | . . . 4 |
10 | an12 525 | . . . . . 6 | |
11 | 10 | mobii 1978 | . . . . 5 |
12 | 11 | albii 1399 | . . . 4 |
13 | 9, 12 | sylib 120 | . . 3 |
14 | moanimv 2016 | . . . 4 | |
15 | 14 | albii 1399 | . . 3 |
16 | 13, 15 | sylib 120 | . 2 |
17 | df-ral 2353 | . . 3 | |
18 | df-rmo 2356 | . . . . 5 | |
19 | 18 | imbi2i 224 | . . . 4 |
20 | 19 | albii 1399 | . . 3 |
21 | 17, 20 | bitri 182 | . 2 |
22 | 16, 21 | sylibr 132 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 102 wal 1282 wex 1421 wcel 1433 wmo 1942 wral 2348 wrex 2349 wrmo 2351 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-io 662 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-10 1436 ax-11 1437 ax-i12 1438 ax-bndl 1439 ax-4 1440 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 |
This theorem depends on definitions: df-bi 115 df-tru 1287 df-nf 1390 df-sb 1686 df-eu 1944 df-mo 1945 df-ral 2353 df-rex 2354 df-rmo 2356 |
This theorem is referenced by: (None) |
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