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Mirrors > Home > ILE Home > Th. List > cbvexdh | Unicode version |
Description: Deduction used to change bound variables, using implicit substitition, particularly useful in conjunction with dvelim 1893. (Contributed by NM, 2-Jan-2002.) (Proof rewritten by Jim Kingdon, 30-Dec-2017.) |
Ref | Expression |
---|---|
cbvexdh.1 | |
cbvexdh.2 | |
cbvexdh.3 |
Ref | Expression |
---|---|
cbvexdh |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax-17 1419 | . . 3 | |
2 | ax-17 1419 | . . . 4 | |
3 | 2 | hbex 1527 | . . 3 |
4 | cbvexdh.1 | . . . . 5 | |
5 | cbvexdh.2 | . . . . 5 | |
6 | cbvexdh.3 | . . . . . 6 | |
7 | equcomi 1592 | . . . . . . 7 | |
8 | bicom1 122 | . . . . . . 7 | |
9 | 7, 8 | imim12i 53 | . . . . . 6 |
10 | 6, 9 | syl 14 | . . . . 5 |
11 | 4, 5, 10 | equsexd 1617 | . . . 4 |
12 | simpr 103 | . . . . 5 | |
13 | 12 | eximi 1491 | . . . 4 |
14 | 11, 13 | syl6bir 153 | . . 3 |
15 | 1, 3, 14 | exlimdh 1487 | . 2 |
16 | 1, 5 | eximdh 1502 | . . . 4 |
17 | 19.12 1555 | . . . 4 | |
18 | 16, 17 | syl6 29 | . . 3 |
19 | 2 | a1i 9 | . . . . 5 |
20 | 1, 19, 6 | equsexd 1617 | . . . 4 |
21 | simpr 103 | . . . . 5 | |
22 | 21 | eximi 1491 | . . . 4 |
23 | 20, 22 | syl6bir 153 | . . 3 |
24 | 4, 18, 23 | exlimd2 1486 | . 2 |
25 | 15, 24 | 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-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 |
This theorem depends on definitions: df-bi 110 |
This theorem is referenced by: cbvexd 1802 |
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