Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > 2exsb | Unicode version |
Description: An equivalent expression for double existence. (Contributed by NM, 2-Feb-2005.) |
Ref | Expression |
---|---|
2exsb |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | exsb 1983 | . . . 4 | |
2 | 1 | exbii 1584 | . . 3 |
3 | excom 1642 | . . 3 | |
4 | 2, 3 | bitri 183 | . 2 |
5 | exsb 1983 | . . . 4 | |
6 | impexp 261 | . . . . . . . 8 | |
7 | 6 | albii 1446 | . . . . . . 7 |
8 | 19.21v 1845 | . . . . . . 7 | |
9 | 7, 8 | bitr2i 184 | . . . . . 6 |
10 | 9 | albii 1446 | . . . . 5 |
11 | 10 | exbii 1584 | . . . 4 |
12 | 5, 11 | bitri 183 | . . 3 |
13 | 12 | exbii 1584 | . 2 |
14 | excom 1642 | . 2 | |
15 | 4, 13, 14 | 3bitri 205 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wal 1329 wex 1468 |
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-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-11 1484 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 |
This theorem depends on definitions: df-bi 116 df-sb 1736 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |