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Mirrors > Home > ILE Home > Th. List > cbvsumi | Unicode version |
Description: Change bound variable in a sum. (Contributed by NM, 11-Dec-2005.) |
Ref | Expression |
---|---|
cbvsumi.1 |
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cbvsumi.2 |
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cbvsumi.3 |
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Ref | Expression |
---|---|
cbvsumi |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cbvsumi.3 |
. 2
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2 | nfcv 2332 |
. 2
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3 | nfcv 2332 |
. 2
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4 | cbvsumi.1 |
. 2
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5 | cbvsumi.2 |
. 2
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6 | 1, 2, 3, 4, 5 | cbvsum 11403 |
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 710 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-10 1516 ax-11 1517 ax-i12 1518 ax-bndl 1520 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-ext 2171 |
This theorem depends on definitions: df-bi 117 df-3an 982 df-tru 1367 df-nf 1472 df-sb 1774 df-clab 2176 df-cleq 2182 df-clel 2185 df-nfc 2321 df-ral 2473 df-rex 2474 df-rab 2477 df-v 2754 df-sbc 2978 df-csb 3073 df-un 3148 df-in 3150 df-ss 3157 df-if 3550 df-sn 3613 df-pr 3614 df-op 3616 df-uni 3825 df-br 4019 df-opab 4080 df-mpt 4081 df-cnv 4652 df-dm 4654 df-rn 4655 df-res 4656 df-iota 5196 df-fv 5243 df-ov 5900 df-oprab 5901 df-mpo 5902 df-recs 6331 df-frec 6417 df-seqfrec 10479 df-sumdc 11397 |
This theorem is referenced by: sumfct 11417 isumss2 11436 fsumzcl2 11448 fsumsplitf 11451 sumsnf 11452 sumsns 11458 fsumsplitsnun 11462 fsum2dlemstep 11477 fisumcom2 11481 fsumshftm 11488 fsumiun 11520 |
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