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Mirrors > Home > ILE Home > Th. List > euan | Unicode version |
Description: Introduction of a conjunct into uniqueness quantifier. (Contributed by NM, 19-Feb-2005.) (Proof shortened by Andrew Salmon, 9-Jul-2011.) |
Ref | Expression |
---|---|
euan.1 |
Ref | Expression |
---|---|
euan |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | euan.1 | . . . . . 6 | |
2 | simpl 102 | . . . . . 6 | |
3 | 1, 2 | exlimih 1484 | . . . . 5 |
4 | 3 | adantr 261 | . . . 4 |
5 | simpr 103 | . . . . . 6 | |
6 | 5 | eximi 1491 | . . . . 5 |
7 | 6 | adantr 261 | . . . 4 |
8 | hbe1 1384 | . . . . . 6 | |
9 | 3 | a1d 22 | . . . . . . . 8 |
10 | 9 | ancrd 309 | . . . . . . 7 |
11 | 5, 10 | impbid2 131 | . . . . . 6 |
12 | 8, 11 | mobidh 1934 | . . . . 5 |
13 | 12 | biimpa 280 | . . . 4 |
14 | 4, 7, 13 | jca32 293 | . . 3 |
15 | eu5 1947 | . . 3 | |
16 | eu5 1947 | . . . 4 | |
17 | 16 | anbi2i 430 | . . 3 |
18 | 14, 15, 17 | 3imtr4i 190 | . 2 |
19 | ibar 285 | . . . 4 | |
20 | 1, 19 | eubidh 1906 | . . 3 |
21 | 20 | biimpa 280 | . 2 |
22 | 18, 21 | impbii 117 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 wb 98 wal 1241 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-nf 1350 df-sb 1646 df-eu 1903 df-mo 1904 |
This theorem is referenced by: euanv 1957 2eu7 1994 |
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