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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 |
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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 2177 |
. . . . 5
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2 | sbequ12 1727 |
. . . . 5
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3 | 1, 2 | anbi12d 462 |
. . . 4
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4 | nfv 1491 |
. . . 4
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5 | nfv 1491 |
. . . . 5
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6 | nfs1v 1890 |
. . . . 5
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7 | 5, 6 | nfan 1527 |
. . . 4
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8 | 3, 4, 7 | cbviota 5051 |
. . 3
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9 | eleq1 2177 |
. . . . 5
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10 | sbequ 1794 |
. . . . . 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 1747 |
. . . . . 6
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14 | 10, 13 | syl6bb 195 |
. . . . 5
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15 | 9, 14 | anbi12d 462 |
. . . 4
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16 | nfv 1491 |
. . . . 5
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17 | cbvriota.1 |
. . . . . 6
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18 | 17 | nfsb 1897 |
. . . . 5
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19 | 16, 18 | nfan 1527 |
. . . 4
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20 | nfv 1491 |
. . . 4
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21 | 15, 19, 20 | cbviota 5051 |
. . 3
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22 | 8, 21 | eqtri 2135 |
. 2
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23 | df-riota 5684 |
. 2
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24 | df-riota 5684 |
. 2
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25 | 22, 23, 24 | 3eqtr4i 2145 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 681 ax-5 1406 ax-7 1407 ax-gen 1408 ax-ie1 1452 ax-ie2 1453 ax-8 1465 ax-10 1466 ax-11 1467 ax-i12 1468 ax-bndl 1469 ax-4 1470 ax-17 1489 ax-i9 1493 ax-ial 1497 ax-i5r 1498 ax-ext 2097 |
This theorem depends on definitions: df-bi 116 df-tru 1317 df-nf 1420 df-sb 1719 df-clab 2102 df-cleq 2108 df-clel 2111 df-nfc 2244 df-rex 2396 df-sn 3499 df-uni 3703 df-iota 5046 df-riota 5684 |
This theorem is referenced by: cbvriotav 5695 |
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