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Mirrors > Home > ILE Home > Th. List > euan | Unicode version |
Description: Introduction of a conjunct into unique existential 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 108 | . . . . . 6 | |
3 | 1, 2 | exlimih 1586 | . . . . 5 |
4 | 3 | adantr 274 | . . . 4 |
5 | simpr 109 | . . . . . 6 | |
6 | 5 | eximi 1593 | . . . . 5 |
7 | 6 | adantr 274 | . . . 4 |
8 | hbe1 1488 | . . . . . 6 | |
9 | 3 | a1d 22 | . . . . . . . 8 |
10 | 9 | ancrd 324 | . . . . . . 7 |
11 | 5, 10 | impbid2 142 | . . . . . 6 |
12 | 8, 11 | mobidh 2053 | . . . . 5 |
13 | 12 | biimpa 294 | . . . 4 |
14 | 4, 7, 13 | jca32 308 | . . 3 |
15 | eu5 2066 | . . 3 | |
16 | eu5 2066 | . . . 4 | |
17 | 16 | anbi2i 454 | . . 3 |
18 | 14, 15, 17 | 3imtr4i 200 | . 2 |
19 | ibar 299 | . . . 4 | |
20 | 1, 19 | eubidh 2025 | . . 3 |
21 | 20 | biimpa 294 | . 2 |
22 | 18, 21 | impbii 125 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wal 1346 wex 1485 weu 2019 wmo 2020 |
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 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 |
This theorem depends on definitions: df-bi 116 df-nf 1454 df-sb 1756 df-eu 2022 df-mo 2023 |
This theorem is referenced by: euanv 2076 2eu7 2113 |
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