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Mirrors > Home > ILE Home > Th. List > cbvsumv | Unicode version |
Description: Change bound variable in a sum. (Contributed by NM, 11-Dec-2005.) (Revised by Mario Carneiro, 13-Jul-2013.) |
Ref | Expression |
---|---|
cbvsum.1 |
Ref | Expression |
---|---|
cbvsumv |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cbvsum.1 | . 2 | |
2 | nfcv 2279 | . 2 | |
3 | nfcv 2279 | . 2 | |
4 | nfcv 2279 | . 2 | |
5 | nfcv 2279 | . 2 | |
6 | 1, 2, 3, 4, 5 | cbvsum 11122 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1331 csu 11115 |
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 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2119 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2124 df-cleq 2130 df-clel 2133 df-nfc 2268 df-ral 2419 df-rex 2420 df-rab 2423 df-v 2683 df-sbc 2905 df-csb 2999 df-un 3070 df-in 3072 df-ss 3079 df-if 3470 df-sn 3528 df-pr 3529 df-op 3531 df-uni 3732 df-br 3925 df-opab 3985 df-mpt 3986 df-cnv 4542 df-dm 4544 df-rn 4545 df-res 4546 df-iota 5083 df-fv 5126 df-ov 5770 df-oprab 5771 df-mpo 5772 df-recs 6195 df-frec 6281 df-seqfrec 10212 df-sumdc 11116 |
This theorem is referenced by: isumge0 11192 telfsumo 11228 fsumparts 11232 binomlem 11245 mertenslemi1 11297 mertenslem2 11298 mertensabs 11299 efaddlem 11369 trilpo 13225 |
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