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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 1471 | . 2 | |
2 | gencbval.1 | . . . 4 | |
3 | gencbval.3 | . . . . . . 7 | |
4 | gencbval.2 | . . . . . . 7 | |
5 | 3, 4 | imbi12d 233 | . . . . . 6 |
6 | 5 | bicomd 140 | . . . . 5 |
7 | 6 | eqcoms 2173 | . . . 4 |
8 | 2, 7 | ceqsalv 2760 | . . 3 |
9 | 8 | albii 1463 | . 2 |
10 | 19.23v 1876 | . . . 4 | |
11 | gencbval.4 | . . . . . . 7 | |
12 | eqcom 2172 | . . . . . . . . . 10 | |
13 | 12 | biimpi 119 | . . . . . . . . 9 |
14 | 13 | adantl 275 | . . . . . . . 8 |
15 | 14 | eximi 1593 | . . . . . . 7 |
16 | 11, 15 | sylbi 120 | . . . . . 6 |
17 | pm2.04 82 | . . . . . 6 | |
18 | 16, 17 | mpdi 43 | . . . . 5 |
19 | ax-1 6 | . . . . 5 | |
20 | 18, 19 | impbii 125 | . . . 4 |
21 | 10, 20 | bitri 183 | . . 3 |
22 | 21 | albii 1463 | . 2 |
23 | 1, 9, 22 | 3bitr3i 209 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wal 1346 wceq 1348 wex 1485 wcel 2141 cvv 2730 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-ext 2152 |
This theorem depends on definitions: df-bi 116 df-nf 1454 df-sb 1756 df-clab 2157 df-cleq 2163 df-clel 2166 df-v 2732 |
This theorem is referenced by: (None) |
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