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Mirrors > Home > ILE Home > Th. List > equsexd | Unicode version |
Description: Deduction form of equsex 1616. (Contributed by Jim Kingdon, 29-Dec-2017.) |
Ref | Expression |
---|---|
equsexd.1 | |
equsexd.2 | |
equsexd.3 |
Ref | Expression |
---|---|
equsexd |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | equsexd.1 | . . 3 | |
2 | equsexd.2 | . . 3 | |
3 | equsexd.3 | . . . 4 | |
4 | bi1 111 | . . . . 5 | |
5 | 4 | imim2i 12 | . . . 4 |
6 | pm3.31 249 | . . . 4 | |
7 | 3, 5, 6 | 3syl 17 | . . 3 |
8 | 1, 2, 7 | exlimd2 1486 | . 2 |
9 | a9e 1586 | . . . 4 | |
10 | 1 | a1i 9 | . . . . . . . . 9 |
11 | 10, 2 | jca 290 | . . . . . . . 8 |
12 | prth 326 | . . . . . . . 8 | |
13 | 11, 12 | syl 14 | . . . . . . 7 |
14 | 19.26 1370 | . . . . . . 7 | |
15 | 13, 14 | syl6ibr 151 | . . . . . 6 |
16 | 15 | anabsi5 513 | . . . . 5 |
17 | idd 21 | . . . . . . . 8 | |
18 | 17 | a1i 9 | . . . . . . 7 |
19 | 18 | imp 115 | . . . . . 6 |
20 | bi2 121 | . . . . . . . . 9 | |
21 | 20 | imim2i 12 | . . . . . . . 8 |
22 | pm2.04 76 | . . . . . . . 8 | |
23 | 3, 21, 22 | 3syl 17 | . . . . . . 7 |
24 | 23 | imp 115 | . . . . . 6 |
25 | 19, 24 | jcad 291 | . . . . 5 |
26 | 16, 25 | eximdh 1502 | . . . 4 |
27 | 9, 26 | mpi 15 | . . 3 |
28 | 27 | ex 108 | . 2 |
29 | 8, 28 | impbid 120 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 wb 98 wal 1241 wceq 1243 wex 1381 |
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-5 1336 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-4 1400 ax-i9 1423 ax-ial 1427 |
This theorem depends on definitions: df-bi 110 |
This theorem is referenced by: cbvexdh 1801 |
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