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Mirrors > Home > MPE Home > Th. List > cbvriota | Structured version Visualization version 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 2689 | . . . . 5 | |
2 | sbequ12 2111 | . . . . 5 | |
3 | 1, 2 | anbi12d 747 | . . . 4 |
4 | nfv 1843 | . . . 4 | |
5 | nfv 1843 | . . . . 5 | |
6 | nfs1v 2437 | . . . . 5 | |
7 | 5, 6 | nfan 1828 | . . . 4 |
8 | 3, 4, 7 | cbviota 5856 | . . 3 |
9 | eleq1 2689 | . . . . 5 | |
10 | sbequ 2376 | . . . . . 6 | |
11 | cbvriota.2 | . . . . . . 7 | |
12 | cbvriota.3 | . . . . . . 7 | |
13 | 11, 12 | sbie 2408 | . . . . . 6 |
14 | 10, 13 | syl6bb 276 | . . . . 5 |
15 | 9, 14 | anbi12d 747 | . . . 4 |
16 | nfv 1843 | . . . . 5 | |
17 | cbvriota.1 | . . . . . 6 | |
18 | 17 | nfsb 2440 | . . . . 5 |
19 | 16, 18 | nfan 1828 | . . . 4 |
20 | nfv 1843 | . . . 4 | |
21 | 15, 19, 20 | cbviota 5856 | . . 3 |
22 | 8, 21 | eqtri 2644 | . 2 |
23 | df-riota 6611 | . 2 | |
24 | df-riota 6611 | . 2 | |
25 | 22, 23, 24 | 3eqtr4i 2654 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 196 wa 384 wceq 1483 wnf 1708 wsb 1880 wcel 1990 cio 5849 crio 6610 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-rex 2918 df-sn 4178 df-uni 4437 df-iota 5851 df-riota 6611 |
This theorem is referenced by: cbvriotav 6622 disjinfi 39380 |
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