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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 4078 |
. . 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 4078 |
. . 3
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25 | 8, 24 | eqtri 2198 |
. 2
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26 | df-mpt 4068 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
27 | df-mpt 4068 |
. 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 2741 df-un 3135 df-sn 3600 df-pr 3601 df-op 3603 df-opab 4067 df-mpt 4068 |
This theorem is referenced by: cbvmptv 4101 dffn5imf 5573 fvmpts 5596 fvmpt2 5601 mptfvex 5603 fmptcof 5685 fmptcos 5686 fliftfuns 5801 offval2 6100 qliftfuns 6621 cc2 7268 summodclem2a 11391 zsumdc 11394 fsum3cvg2 11404 cbvprod 11568 zproddc 11589 fprodseq 11593 pcmptdvds 12345 cnmpt1t 13870 fsumcncntop 14141 limcmpted 14217 |
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