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Mirrors > Home > ILE Home > Th. List > gencbval | Unicode version |
Description: Change of bound variable using implicit substitution. (Contributed by NM, 17-May-1996.) (Proof rewritten by Jim Kingdon, 20-Jun-2018.) |
Ref | Expression |
---|---|
gencbval.1 | |
gencbval.2 | |
gencbval.3 | |
gencbval.4 |
Ref | Expression |
---|---|
gencbval |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | alcom 1407 | . 2 | |
2 | gencbval.1 | . . . 4 | |
3 | gencbval.3 | . . . . . . 7 | |
4 | gencbval.2 | . . . . . . 7 | |
5 | 3, 4 | imbi12d 232 | . . . . . 6 |
6 | 5 | bicomd 139 | . . . . 5 |
7 | 6 | eqcoms 2084 | . . . 4 |
8 | 2, 7 | ceqsalv 2629 | . . 3 |
9 | 8 | albii 1399 | . 2 |
10 | 19.23v 1804 | . . . 4 | |
11 | gencbval.4 | . . . . . . 7 | |
12 | eqcom 2083 | . . . . . . . . . 10 | |
13 | 12 | biimpi 118 | . . . . . . . . 9 |
14 | 13 | adantl 271 | . . . . . . . 8 |
15 | 14 | eximi 1531 | . . . . . . 7 |
16 | 11, 15 | sylbi 119 | . . . . . 6 |
17 | pm2.04 81 | . . . . . 6 | |
18 | 16, 17 | mpdi 42 | . . . . 5 |
19 | ax-1 5 | . . . . 5 | |
20 | 18, 19 | impbii 124 | . . . 4 |
21 | 10, 20 | bitri 182 | . . 3 |
22 | 21 | albii 1399 | . 2 |
23 | 1, 9, 22 | 3bitr3i 208 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 102 wb 103 wal 1282 wceq 1284 wex 1421 wcel 1433 cvv 2601 |
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 ax-ext 2063 |
This theorem depends on definitions: df-bi 115 df-nf 1390 df-sb 1686 df-clab 2068 df-cleq 2074 df-clel 2077 df-v 2603 |
This theorem is referenced by: (None) |
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