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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 1925 | . . . 4 | |
2 | 1 | exbii 1536 | . . 3 |
3 | excom 1594 | . . 3 | |
4 | 2, 3 | bitri 182 | . 2 |
5 | exsb 1925 | . . . 4 | |
6 | impexp 259 | . . . . . . . 8 | |
7 | 6 | albii 1399 | . . . . . . 7 |
8 | 19.21v 1794 | . . . . . . 7 | |
9 | 7, 8 | bitr2i 183 | . . . . . 6 |
10 | 9 | albii 1399 | . . . . 5 |
11 | 10 | exbii 1536 | . . . 4 |
12 | 5, 11 | bitri 182 | . . 3 |
13 | 12 | exbii 1536 | . 2 |
14 | excom 1594 | . 2 | |
15 | 4, 13, 14 | 3bitri 204 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 102 wb 103 wal 1282 wex 1421 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-11 1437 ax-4 1440 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 |
This theorem depends on definitions: df-bi 115 df-sb 1686 |
This theorem is referenced by: (None) |
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