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Mirrors > Home > ILE Home > Th. List > cbvrab | Unicode version |
Description: Rule to change the bound variable in a restricted class abstraction, using implicit substitution. This version has bound-variable hypotheses in place of distinct variable conditions. (Contributed by Andrew Salmon, 11-Jul-2011.) (Revised by Mario Carneiro, 9-Oct-2016.) |
Ref | Expression |
---|---|
cbvrab.1 |
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cbvrab.2 |
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cbvrab.3 |
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cbvrab.4 |
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cbvrab.5 |
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Ref | Expression |
---|---|
cbvrab |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfv 1509 |
. . . 4
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2 | cbvrab.1 |
. . . . . 6
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3 | 2 | nfcri 2276 |
. . . . 5
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4 | nfs1v 1913 |
. . . . 5
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5 | 3, 4 | nfan 1545 |
. . . 4
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6 | eleq1 2203 |
. . . . 5
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7 | sbequ12 1745 |
. . . . 5
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8 | 6, 7 | anbi12d 465 |
. . . 4
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9 | 1, 5, 8 | cbvab 2264 |
. . 3
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10 | cbvrab.2 |
. . . . . 6
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11 | 10 | nfcri 2276 |
. . . . 5
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12 | cbvrab.3 |
. . . . . 6
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13 | 12 | nfsb 1920 |
. . . . 5
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14 | 11, 13 | nfan 1545 |
. . . 4
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15 | nfv 1509 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
16 | eleq1 2203 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
17 | sbequ 1813 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
18 | cbvrab.4 |
. . . . . . 7
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19 | cbvrab.5 |
. . . . . . 7
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20 | 18, 19 | sbie 1765 |
. . . . . 6
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21 | 17, 20 | syl6bb 195 |
. . . . 5
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22 | 16, 21 | anbi12d 465 |
. . . 4
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23 | 14, 15, 22 | cbvab 2264 |
. . 3
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24 | 9, 23 | eqtri 2161 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
25 | df-rab 2426 |
. 2
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26 | df-rab 2426 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
27 | 24, 25, 26 | 3eqtr4i 2171 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
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 699 ax-5 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-10 1484 ax-11 1485 ax-i12 1486 ax-bndl 1487 ax-4 1488 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 |
This theorem depends on definitions: df-bi 116 df-nf 1438 df-sb 1737 df-clab 2127 df-cleq 2133 df-clel 2136 df-nfc 2271 df-rab 2426 |
This theorem is referenced by: cbvrabv 2688 elrabsf 2951 tfis 4505 |
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