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Mirrors > Home > ILE Home > Th. List > Mathboxes > cbvrald | Unicode version |
Description: Rule used to change bound variables, using implicit substitution. (Contributed by BJ, 22-Nov-2019.) |
Ref | Expression |
---|---|
cbvrald.nf0 | |
cbvrald.nf1 | |
cbvrald.nf2 | |
cbvrald.nf3 | |
cbvrald.is |
Ref | Expression |
---|---|
cbvrald |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cbvrald.nf0 | . . . 4 | |
2 | nfv 1521 | . . . 4 | |
3 | nfv 1521 | . . . . . 6 | |
4 | 3 | a1i 9 | . . . . 5 |
5 | nfv 1521 | . . . . . 6 | |
6 | 5 | a1i 9 | . . . . 5 |
7 | 4, 6 | nfimd 1578 | . . . 4 |
8 | nfv 1521 | . . . . . 6 | |
9 | 8 | a1i 9 | . . . . 5 |
10 | nfs1v 1932 | . . . . . 6 | |
11 | 10 | a1i 9 | . . . . 5 |
12 | 9, 11 | nfimd 1578 | . . . 4 |
13 | eleq1 2233 | . . . . . . 7 | |
14 | 13 | adantl 275 | . . . . . 6 |
15 | sbequ12 1764 | . . . . . . 7 | |
16 | 15 | adantl 275 | . . . . . 6 |
17 | 14, 16 | imbi12d 233 | . . . . 5 |
18 | 17 | ex 114 | . . . 4 |
19 | 1, 2, 7, 12, 18 | cbv2 1742 | . . 3 |
20 | cbvrald.nf1 | . . . 4 | |
21 | nfv 1521 | . . . . . 6 | |
22 | 21 | a1i 9 | . . . . 5 |
23 | cbvrald.nf2 | . . . . . 6 | |
24 | 1, 23 | nfsbd 1970 | . . . . 5 |
25 | 22, 24 | nfimd 1578 | . . . 4 |
26 | nfv 1521 | . . . . . 6 | |
27 | 26 | a1i 9 | . . . . 5 |
28 | nfv 1521 | . . . . . 6 | |
29 | 28 | a1i 9 | . . . . 5 |
30 | 27, 29 | nfimd 1578 | . . . 4 |
31 | eleq1 2233 | . . . . . . 7 | |
32 | 31 | adantl 275 | . . . . . 6 |
33 | sbequ 1833 | . . . . . . 7 | |
34 | cbvrald.nf3 | . . . . . . . 8 | |
35 | cbvrald.is | . . . . . . . 8 | |
36 | 1, 34, 35 | sbied 1781 | . . . . . . 7 |
37 | 33, 36 | sylan9bbr 460 | . . . . . 6 |
38 | 32, 37 | imbi12d 233 | . . . . 5 |
39 | 38 | ex 114 | . . . 4 |
40 | 2, 20, 25, 30, 39 | cbv2 1742 | . . 3 |
41 | 19, 40 | bitrd 187 | . 2 |
42 | df-ral 2453 | . 2 | |
43 | df-ral 2453 | . 2 | |
44 | 41, 42, 43 | 3bitr4g 222 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wal 1346 wnf 1453 wsb 1755 wcel 2141 wral 2448 |
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-io 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-ext 2152 |
This theorem depends on definitions: df-bi 116 df-nf 1454 df-sb 1756 df-cleq 2163 df-clel 2166 df-ral 2453 |
This theorem is referenced by: setindft 13960 |
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