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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 1367 | . 2 | |
2 | gencbval.1 | . . . 4 | |
3 | gencbval.3 | . . . . . . 7 | |
4 | gencbval.2 | . . . . . . 7 | |
5 | 3, 4 | imbi12d 223 | . . . . . 6 |
6 | 5 | bicomd 129 | . . . . 5 |
7 | 6 | eqcoms 2043 | . . . 4 |
8 | 2, 7 | ceqsalv 2584 | . . 3 |
9 | 8 | albii 1359 | . 2 |
10 | 19.23v 1763 | . . . 4 | |
11 | gencbval.4 | . . . . . . 7 | |
12 | eqcom 2042 | . . . . . . . . . 10 | |
13 | 12 | biimpi 113 | . . . . . . . . 9 |
14 | 13 | adantl 262 | . . . . . . . 8 |
15 | 14 | eximi 1491 | . . . . . . 7 |
16 | 11, 15 | sylbi 114 | . . . . . 6 |
17 | pm2.04 76 | . . . . . 6 | |
18 | 16, 17 | mpdi 38 | . . . . 5 |
19 | ax-1 5 | . . . . 5 | |
20 | 18, 19 | impbii 117 | . . . 4 |
21 | 10, 20 | bitri 173 | . . 3 |
22 | 21 | albii 1359 | . 2 |
23 | 1, 9, 22 | 3bitr3i 199 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 wb 98 wal 1241 wceq 1243 wex 1381 wcel 1393 cvv 2557 |
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 ax-ext 2022 |
This theorem depends on definitions: df-bi 110 df-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-v 2559 |
This theorem is referenced by: (None) |
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