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Mirrors > Home > ILE Home > Th. List > 2exeu | Unicode version |
Description: Double existential uniqueness implies double uniqueness quantification. (Contributed by NM, 3-Dec-2001.) |
Ref | Expression |
---|---|
2exeu |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | excom 1554 | . . . . 5 | |
2 | hbe1 1384 | . . . . . . . 8 | |
3 | 2 | hbmo 1939 | . . . . . . 7 |
4 | 3 | 19.41h 1575 | . . . . . 6 |
5 | 19.8a 1482 | . . . . . . . . 9 | |
6 | 5 | moimi 1965 | . . . . . . . 8 |
7 | 6 | anim2i 324 | . . . . . . 7 |
8 | 7 | eximi 1491 | . . . . . 6 |
9 | 4, 8 | sylbir 125 | . . . . 5 |
10 | 1, 9 | sylanb 268 | . . . 4 |
11 | simpl 102 | . . . . . 6 | |
12 | 11 | moimi 1965 | . . . . 5 |
13 | 12 | adantl 262 | . . . 4 |
14 | 10, 13 | anim12i 321 | . . 3 |
15 | 14 | ancoms 255 | . 2 |
16 | eu5 1947 | . . 3 | |
17 | eu5 1947 | . . 3 | |
18 | 16, 17 | anbi12i 433 | . 2 |
19 | eu5 1947 | . . 3 | |
20 | eu5 1947 | . . . . 5 | |
21 | 20 | exbii 1496 | . . . 4 |
22 | 20 | mobii 1937 | . . . 4 |
23 | 21, 22 | anbi12i 433 | . . 3 |
24 | 19, 23 | bitri 173 | . 2 |
25 | 15, 18, 24 | 3imtr4i 190 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 wex 1381 weu 1900 wmo 1901 |
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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