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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 107 | . . . . . 6 | |
3 | 1, 2 | exlimih 1524 | . . . . 5 |
4 | 3 | adantr 270 | . . . 4 |
5 | simpr 108 | . . . . . 6 | |
6 | 5 | eximi 1531 | . . . . 5 |
7 | 6 | adantr 270 | . . . 4 |
8 | hbe1 1424 | . . . . . 6 | |
9 | 3 | a1d 22 | . . . . . . . 8 |
10 | 9 | ancrd 319 | . . . . . . 7 |
11 | 5, 10 | impbid2 141 | . . . . . 6 |
12 | 8, 11 | mobidh 1975 | . . . . 5 |
13 | 12 | biimpa 290 | . . . 4 |
14 | 4, 7, 13 | jca32 303 | . . 3 |
15 | eu5 1988 | . . 3 | |
16 | eu5 1988 | . . . 4 | |
17 | 16 | anbi2i 444 | . . 3 |
18 | 14, 15, 17 | 3imtr4i 199 | . 2 |
19 | ibar 295 | . . . 4 | |
20 | 1, 19 | eubidh 1947 | . . 3 |
21 | 20 | biimpa 290 | . 2 |
22 | 18, 21 | impbii 124 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 102 wb 103 wal 1282 wex 1421 weu 1941 wmo 1942 |
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-io 662 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-10 1436 ax-11 1437 ax-i12 1438 ax-bndl 1439 ax-4 1440 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 |
This theorem depends on definitions: df-bi 115 df-nf 1390 df-sb 1686 df-eu 1944 df-mo 1945 |
This theorem is referenced by: euanv 1998 2eu7 2035 |
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