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Mirrors > Home > ILE Home > Th. List > 2moswapdc | Unicode version |
Description: A condition allowing swap of "at most one" and existential quantifiers. (Contributed by Jim Kingdon, 6-Jul-2018.) |
Ref | Expression |
---|---|
2moswapdc | DECID |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfe1 1489 | . . . 4 | |
2 | 1 | moexexdc 2103 | . . 3 DECID |
3 | 2 | expcomd 1434 | . 2 DECID |
4 | 19.8a 1583 | . . . . . 6 | |
5 | 4 | pm4.71ri 390 | . . . . 5 |
6 | 5 | exbii 1598 | . . . 4 |
7 | 6 | mobii 2056 | . . 3 |
8 | 7 | imbi2i 225 | . 2 |
9 | 3, 8 | syl6ibr 161 | 1 DECID |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 DECID wdc 829 wal 1346 wex 1485 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-in1 609 ax-in2 610 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-dc 830 df-tru 1351 df-nf 1454 df-sb 1756 df-eu 2022 df-mo 2023 |
This theorem is referenced by: 2euswapdc 2110 |
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