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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 |
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cbvriota.2 |
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cbvriota.3 |
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Ref | Expression |
---|---|
cbvriota |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eleq1 2528 |
. . . . 5
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2 | sbequ12 2094 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
3 | 1, 2 | anbi12d 722 |
. . . 4
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4 | nfv 1772 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
5 | nfv 1772 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() | |
6 | nfs1v 2277 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
7 | 5, 6 | nfan 2022 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
8 | 3, 4, 7 | cbviota 5570 |
. . 3
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9 | eleq1 2528 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
10 | sbequ 2216 |
. . . . . 6
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11 | cbvriota.2 |
. . . . . . 7
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12 | cbvriota.3 |
. . . . . . 7
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13 | 11, 12 | sbie 2248 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
14 | 10, 13 | syl6bb 269 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
15 | 9, 14 | anbi12d 722 |
. . . 4
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16 | nfv 1772 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() | |
17 | cbvriota.1 |
. . . . . 6
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18 | 17 | nfsb 2280 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
19 | 16, 18 | nfan 2022 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
20 | nfv 1772 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
21 | 15, 19, 20 | cbviota 5570 |
. . 3
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22 | 8, 21 | eqtri 2484 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
23 | df-riota 6277 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
24 | df-riota 6277 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
25 | 22, 23, 24 | 3eqtr4i 2494 |
1
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Colors of variables: wff setvar class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1680 ax-4 1693 ax-5 1769 ax-6 1816 ax-7 1862 ax-10 1926 ax-11 1931 ax-12 1944 ax-13 2102 ax-ext 2442 |
This theorem depends on definitions: df-bi 190 df-or 376 df-an 377 df-tru 1458 df-ex 1675 df-nf 1679 df-sb 1809 df-clab 2449 df-cleq 2455 df-clel 2458 df-nfc 2592 df-rex 2755 df-sn 3981 df-uni 4213 df-iota 5565 df-riota 6277 |
This theorem is referenced by: cbvriotav 6288 disjinfi 37506 |
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