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Mirrors > Home > ILE Home > Th. List > 2exeu | Unicode version |
Description: Double existential uniqueness implies double unique existential quantification. (Contributed by NM, 3-Dec-2001.) |
Ref | Expression |
---|---|
2exeu |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | excom 1627 | . . . . 5 | |
2 | hbe1 1456 | . . . . . . . 8 | |
3 | 2 | hbmo 2016 | . . . . . . 7 |
4 | 3 | 19.41h 1648 | . . . . . 6 |
5 | 19.8a 1554 | . . . . . . . . 9 | |
6 | 5 | moimi 2042 | . . . . . . . 8 |
7 | 6 | anim2i 339 | . . . . . . 7 |
8 | 7 | eximi 1564 | . . . . . 6 |
9 | 4, 8 | sylbir 134 | . . . . 5 |
10 | 1, 9 | sylanb 282 | . . . 4 |
11 | simpl 108 | . . . . . 6 | |
12 | 11 | moimi 2042 | . . . . 5 |
13 | 12 | adantl 275 | . . . 4 |
14 | 10, 13 | anim12i 336 | . . 3 |
15 | 14 | ancoms 266 | . 2 |
16 | eu5 2024 | . . 3 | |
17 | eu5 2024 | . . 3 | |
18 | 16, 17 | anbi12i 455 | . 2 |
19 | eu5 2024 | . . 3 | |
20 | eu5 2024 | . . . . 5 | |
21 | 20 | exbii 1569 | . . . 4 |
22 | 20 | mobii 2014 | . . . 4 |
23 | 21, 22 | anbi12i 455 | . . 3 |
24 | 19, 23 | bitri 183 | . 2 |
25 | 15, 18, 24 | 3imtr4i 200 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wex 1453 weu 1977 wmo 1978 |
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-io 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 |
This theorem depends on definitions: df-bi 116 df-tru 1319 df-nf 1422 df-sb 1721 df-eu 1980 df-mo 1981 |
This theorem is referenced by: (None) |
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