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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 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfe1 1473 |
. . . 4
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2 | 1 | moexexdc 2084 |
. . 3
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3 | 2 | expcomd 1418 |
. 2
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4 | 19.8a 1570 |
. . . . . 6
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5 | 4 | pm4.71ri 390 |
. . . . 5
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6 | 5 | exbii 1585 |
. . . 4
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7 | 6 | mobii 2037 |
. . 3
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8 | 7 | imbi2i 225 |
. 2
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9 | 3, 8 | syl6ibr 161 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() |
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 604 ax-in2 605 ax-io 699 ax-5 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-10 1484 ax-11 1485 ax-i12 1486 ax-bndl 1487 ax-4 1488 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 |
This theorem depends on definitions: df-bi 116 df-dc 821 df-tru 1335 df-nf 1438 df-sb 1737 df-eu 2003 df-mo 2004 |
This theorem is referenced by: 2euswapdc 2091 |
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