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Mirrors > Home > ILE Home > Th. List > cbvmpt | Unicode version |
Description: Rule to change the bound variable in a maps-to function, using implicit substitution. This version has bound-variable hypotheses in place of distinct variable conditions. (Contributed by NM, 11-Sep-2011.) |
Ref | Expression |
---|---|
cbvmpt.1 |
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cbvmpt.2 |
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cbvmpt.3 |
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Ref | Expression |
---|---|
cbvmpt |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfv 1528 |
. . . 4
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2 | nfv 1528 |
. . . . 5
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3 | nfs1v 1939 |
. . . . 5
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4 | 2, 3 | nfan 1565 |
. . . 4
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5 | eleq1 2240 |
. . . . 5
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6 | sbequ12 1771 |
. . . . 5
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7 | 5, 6 | anbi12d 473 |
. . . 4
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8 | 1, 4, 7 | cbvopab1 4076 |
. . 3
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9 | nfv 1528 |
. . . . 5
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10 | cbvmpt.1 |
. . . . . . 7
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11 | 10 | nfeq2 2331 |
. . . . . 6
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12 | 11 | nfsb 1946 |
. . . . 5
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13 | 9, 12 | nfan 1565 |
. . . 4
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14 | nfv 1528 |
. . . 4
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15 | eleq1 2240 |
. . . . 5
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16 | sbequ 1840 |
. . . . . 6
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17 | cbvmpt.2 |
. . . . . . . 8
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18 | 17 | nfeq2 2331 |
. . . . . . 7
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19 | cbvmpt.3 |
. . . . . . . 8
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20 | 19 | eqeq2d 2189 |
. . . . . . 7
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21 | 18, 20 | sbie 1791 |
. . . . . 6
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22 | 16, 21 | bitrdi 196 |
. . . . 5
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23 | 15, 22 | anbi12d 473 |
. . . 4
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24 | 13, 14, 23 | cbvopab1 4076 |
. . 3
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25 | 8, 24 | eqtri 2198 |
. 2
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26 | df-mpt 4066 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
27 | df-mpt 4066 |
. 2
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28 | 25, 26, 27 | 3eqtr4i 2208 |
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 106 ax-ia2 107 ax-ia3 108 ax-io 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-ext 2159 |
This theorem depends on definitions: df-bi 117 df-3an 980 df-tru 1356 df-nf 1461 df-sb 1763 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-v 2739 df-un 3133 df-sn 3598 df-pr 3599 df-op 3601 df-opab 4065 df-mpt 4066 |
This theorem is referenced by: cbvmptv 4099 dffn5imf 5571 fvmpts 5594 fvmpt2 5599 mptfvex 5601 fmptcof 5683 fmptcos 5684 fliftfuns 5798 offval2 6097 qliftfuns 6618 cc2 7265 summodclem2a 11384 zsumdc 11387 fsum3cvg2 11397 cbvprod 11561 zproddc 11582 fprodseq 11586 pcmptdvds 12337 cnmpt1t 13716 fsumcncntop 13987 limcmpted 14063 |
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