Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
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 1641 | . . . . 5 | |
2 | 1 | a1i 9 | . . . 4 DECID |
3 | 2moswapdc 2087 | . . . . 5 DECID | |
4 | 3 | imp 123 | . . . 4 DECID |
5 | 2, 4 | anim12d 333 | . . 3 DECID |
6 | eu5 2044 | . . 3 | |
7 | eu5 2044 | . . 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 819 wal 1329 wex 1468 weu 1997 wmo 1998 |
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 603 ax-in2 604 ax-io 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 |
This theorem depends on definitions: df-bi 116 df-dc 820 df-tru 1334 df-nf 1437 df-sb 1736 df-eu 2000 df-mo 2001 |
This theorem is referenced by: euxfr2dc 2864 2reuswapdc 2883 |
Copyright terms: Public domain | W3C validator |