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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 |
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Ref | Expression |
---|---|
cbvsumv |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cbvsum.1 |
. 2
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2 | nfcv 2229 |
. 2
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3 | nfcv 2229 |
. 2
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4 | nfcv 2229 |
. 2
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5 | nfcv 2229 |
. 2
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6 | 1, 2, 3, 4, 5 | cbvsum 10812 |
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 666 ax-5 1382 ax-7 1383 ax-gen 1384 ax-ie1 1428 ax-ie2 1429 ax-8 1441 ax-10 1442 ax-11 1443 ax-i12 1444 ax-bndl 1445 ax-4 1446 ax-17 1465 ax-i9 1469 ax-ial 1473 ax-i5r 1474 ax-ext 2071 |
This theorem depends on definitions: df-bi 116 df-3an 927 df-tru 1293 df-nf 1396 df-sb 1694 df-clab 2076 df-cleq 2082 df-clel 2085 df-nfc 2218 df-ral 2365 df-rex 2366 df-rab 2369 df-v 2624 df-sbc 2844 df-csb 2937 df-un 3006 df-in 3008 df-ss 3015 df-if 3400 df-sn 3458 df-pr 3459 df-op 3461 df-uni 3662 df-br 3854 df-opab 3908 df-mpt 3909 df-cnv 4462 df-dm 4464 df-rn 4465 df-res 4466 df-iota 4995 df-fv 5038 df-ov 5671 df-oprab 5672 df-mpt2 5673 df-recs 6086 df-frec 6172 df-iseq 9916 df-isum 10806 |
This theorem is referenced by: isumge0 10887 telfsumo 10923 fsumparts 10927 binomlem 10940 mertenslemi1 10992 mertenslem2 10993 mertensabs 10994 efaddlem 11027 |
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