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Mirrors > Home > ILE Home > Th. List > 2eu7 | Unicode version |
Description: Two equivalent expressions for double existential uniqueness. (Contributed by NM, 19-Feb-2005.) |
Ref | Expression |
---|---|
2eu7 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | hbe1 1384 | . . . 4 | |
2 | 1 | hbeu 1921 | . . 3 |
3 | 2 | euan 1956 | . 2 |
4 | ancom 253 | . . . . 5 | |
5 | 4 | eubii 1909 | . . . 4 |
6 | hbe1 1384 | . . . . 5 | |
7 | 6 | euan 1956 | . . . 4 |
8 | ancom 253 | . . . 4 | |
9 | 5, 7, 8 | 3bitri 195 | . . 3 |
10 | 9 | eubii 1909 | . 2 |
11 | ancom 253 | . 2 | |
12 | 3, 10, 11 | 3bitr4ri 202 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 97 wb 98 wex 1381 weu 1900 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 |
This theorem depends on definitions: df-bi 110 df-tru 1246 df-nf 1350 df-sb 1646 df-eu 1903 df-mo 1904 |
This theorem is referenced by: (None) |
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