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Mirrors > Home > ILE Home > Th. List > 2euswapdc | Unicode version |
Description: A condition allowing swap of uniqueness and existential quantifiers. (Contributed by Jim Kingdon, 7-Jul-2018.) |
Ref | Expression |
---|---|
2euswapdc | DECID |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | excomim 1643 | . . . . 5 | |
2 | 1 | a1i 9 | . . . 4 DECID |
3 | 2moswapdc 2096 | . . . . 5 DECID | |
4 | 3 | imp 123 | . . . 4 DECID |
5 | 2, 4 | anim12d 333 | . . 3 DECID |
6 | eu5 2053 | . . 3 | |
7 | eu5 2053 | . . 3 | |
8 | 5, 6, 7 | 3imtr4g 204 | . 2 DECID |
9 | 8 | ex 114 | 1 DECID |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 DECID wdc 820 wal 1333 wex 1472 weu 2006 wmo 2007 |
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 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 |
This theorem depends on definitions: df-bi 116 df-dc 821 df-tru 1338 df-nf 1441 df-sb 1743 df-eu 2009 df-mo 2010 |
This theorem is referenced by: euxfr2dc 2897 2reuswapdc 2916 |
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