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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 2202 | . . . . 5 | |
2 | sbequ12 1744 | . . . . 5 | |
3 | 1, 2 | anbi12d 464 | . . . 4 |
4 | nfv 1508 | . . . 4 | |
5 | nfv 1508 | . . . . 5 | |
6 | nfs1v 1912 | . . . . 5 | |
7 | 5, 6 | nfan 1544 | . . . 4 |
8 | 3, 4, 7 | cbviota 5093 | . . 3 |
9 | eleq1 2202 | . . . . 5 | |
10 | sbequ 1812 | . . . . . 6 | |
11 | cbvriota.2 | . . . . . . 7 | |
12 | cbvriota.3 | . . . . . . 7 | |
13 | 11, 12 | sbie 1764 | . . . . . 6 |
14 | 10, 13 | syl6bb 195 | . . . . 5 |
15 | 9, 14 | anbi12d 464 | . . . 4 |
16 | nfv 1508 | . . . . 5 | |
17 | cbvriota.1 | . . . . . 6 | |
18 | 17 | nfsb 1919 | . . . . 5 |
19 | 16, 18 | nfan 1544 | . . . 4 |
20 | nfv 1508 | . . . 4 | |
21 | 15, 19, 20 | cbviota 5093 | . . 3 |
22 | 8, 21 | eqtri 2160 | . 2 |
23 | df-riota 5730 | . 2 | |
24 | df-riota 5730 | . 2 | |
25 | 22, 23, 24 | 3eqtr4i 2170 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wceq 1331 wnf 1436 wcel 1480 wsb 1735 cio 5086 crio 5729 |
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 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 |
This theorem depends on definitions: df-bi 116 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-rex 2422 df-sn 3533 df-uni 3737 df-iota 5088 df-riota 5730 |
This theorem is referenced by: cbvriotav 5741 |
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