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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 1934. (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 1459 | . . 3 | |
2 | ax-17 1459 | . . . 4 | |
3 | 2 | hbex 1567 | . . 3 |
4 | cbvexdh.1 | . . . . 5 | |
5 | cbvexdh.2 | . . . . 5 | |
6 | cbvexdh.3 | . . . . . 6 | |
7 | equcomi 1632 | . . . . . . 7 | |
8 | bicom1 129 | . . . . . . 7 | |
9 | 7, 8 | imim12i 58 | . . . . . 6 |
10 | 6, 9 | syl 14 | . . . . 5 |
11 | 4, 5, 10 | equsexd 1657 | . . . 4 |
12 | simpr 108 | . . . . 5 | |
13 | 12 | eximi 1531 | . . . 4 |
14 | 11, 13 | syl6bir 162 | . . 3 |
15 | 1, 3, 14 | exlimdh 1527 | . 2 |
16 | 1, 5 | eximdh 1542 | . . . 4 |
17 | 19.12 1595 | . . . 4 | |
18 | 16, 17 | syl6 33 | . . 3 |
19 | 2 | a1i 9 | . . . . 5 |
20 | 1, 19, 6 | equsexd 1657 | . . . 4 |
21 | simpr 108 | . . . . 5 | |
22 | 21 | eximi 1531 | . . . 4 |
23 | 20, 22 | syl6bir 162 | . . 3 |
24 | 4, 18, 23 | exlimd2 1526 | . 2 |
25 | 15, 24 | impbid 127 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 102 wb 103 wal 1282 wceq 1284 wex 1421 |
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-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-4 1440 ax-17 1459 ax-i9 1463 ax-ial 1467 |
This theorem depends on definitions: df-bi 115 |
This theorem is referenced by: cbvexd 1843 |
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