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Mirrors > Home > ILE Home > Th. List > cbvriota | Unicode version |
Description: Change bound variable in a restricted description binder. (Contributed by NM, 18-Mar-2013.) (Revised by Mario Carneiro, 15-Oct-2016.) |
Ref | Expression |
---|---|
cbvriota.1 | |
cbvriota.2 | |
cbvriota.3 |
Ref | Expression |
---|---|
cbvriota |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eleq1 2100 | . . . . 5 | |
2 | sbequ12 1654 | . . . . 5 | |
3 | 1, 2 | anbi12d 442 | . . . 4 |
4 | nfv 1421 | . . . 4 | |
5 | nfv 1421 | . . . . 5 | |
6 | nfs1v 1815 | . . . . 5 | |
7 | 5, 6 | nfan 1457 | . . . 4 |
8 | 3, 4, 7 | cbviota 4872 | . . 3 |
9 | eleq1 2100 | . . . . 5 | |
10 | sbequ 1721 | . . . . . 6 | |
11 | cbvriota.2 | . . . . . . 7 | |
12 | cbvriota.3 | . . . . . . 7 | |
13 | 11, 12 | sbie 1674 | . . . . . 6 |
14 | 10, 13 | syl6bb 185 | . . . . 5 |
15 | 9, 14 | anbi12d 442 | . . . 4 |
16 | nfv 1421 | . . . . 5 | |
17 | cbvriota.1 | . . . . . 6 | |
18 | 17 | nfsb 1822 | . . . . 5 |
19 | 16, 18 | nfan 1457 | . . . 4 |
20 | nfv 1421 | . . . 4 | |
21 | 15, 19, 20 | cbviota 4872 | . . 3 |
22 | 8, 21 | eqtri 2060 | . 2 |
23 | df-riota 5468 | . 2 | |
24 | df-riota 5468 | . 2 | |
25 | 22, 23, 24 | 3eqtr4i 2070 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 wb 98 wceq 1243 wnf 1349 wcel 1393 wsb 1645 cio 4865 crio 5467 |
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-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 |
This theorem depends on definitions: df-bi 110 df-tru 1246 df-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-rex 2312 df-sn 3381 df-uni 3581 df-iota 4867 df-riota 5468 |
This theorem is referenced by: cbvriotav 5479 |
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