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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 2141 | . . . . 5 | |
2 | sbequ12 1694 | . . . . 5 | |
3 | 1, 2 | anbi12d 456 | . . . 4 |
4 | nfv 1461 | . . . 4 | |
5 | nfv 1461 | . . . . 5 | |
6 | nfs1v 1856 | . . . . 5 | |
7 | 5, 6 | nfan 1497 | . . . 4 |
8 | 3, 4, 7 | cbviota 4892 | . . 3 |
9 | eleq1 2141 | . . . . 5 | |
10 | sbequ 1761 | . . . . . 6 | |
11 | cbvriota.2 | . . . . . . 7 | |
12 | cbvriota.3 | . . . . . . 7 | |
13 | 11, 12 | sbie 1714 | . . . . . 6 |
14 | 10, 13 | syl6bb 194 | . . . . 5 |
15 | 9, 14 | anbi12d 456 | . . . 4 |
16 | nfv 1461 | . . . . 5 | |
17 | cbvriota.1 | . . . . . 6 | |
18 | 17 | nfsb 1863 | . . . . 5 |
19 | 16, 18 | nfan 1497 | . . . 4 |
20 | nfv 1461 | . . . 4 | |
21 | 15, 19, 20 | cbviota 4892 | . . 3 |
22 | 8, 21 | eqtri 2101 | . 2 |
23 | df-riota 5488 | . 2 | |
24 | df-riota 5488 | . 2 | |
25 | 22, 23, 24 | 3eqtr4i 2111 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 102 wb 103 wceq 1284 wnf 1389 wcel 1433 wsb 1685 cio 4885 crio 5487 |
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-io 662 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-10 1436 ax-11 1437 ax-i12 1438 ax-bndl 1439 ax-4 1440 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 |
This theorem depends on definitions: df-bi 115 df-tru 1287 df-nf 1390 df-sb 1686 df-clab 2068 df-cleq 2074 df-clel 2077 df-nfc 2208 df-rex 2354 df-sn 3404 df-uni 3602 df-iota 4887 df-riota 5488 |
This theorem is referenced by: cbvriotav 5499 |
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