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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 2282 |
. 2
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3 | nfcv 2282 |
. 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 11161 |
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 105 ax-ia2 106 ax-ia3 107 ax-io 699 ax-5 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-10 1484 ax-11 1485 ax-i12 1486 ax-bndl 1487 ax-4 1488 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1335 df-nf 1438 df-sb 1737 df-clab 2127 df-cleq 2133 df-clel 2136 df-nfc 2271 df-ral 2422 df-rex 2423 df-rab 2426 df-v 2691 df-sbc 2914 df-csb 3008 df-un 3080 df-in 3082 df-ss 3089 df-if 3480 df-sn 3538 df-pr 3539 df-op 3541 df-uni 3745 df-br 3938 df-opab 3998 df-mpt 3999 df-cnv 4555 df-dm 4557 df-rn 4558 df-res 4559 df-iota 5096 df-fv 5139 df-ov 5785 df-oprab 5786 df-mpo 5787 df-recs 6210 df-frec 6296 df-seqfrec 10250 df-sumdc 11155 |
This theorem is referenced by: sumfct 11175 isumss2 11194 fsumzcl2 11206 fsumsplitf 11209 sumsnf 11210 sumsns 11216 fsumsplitsnun 11220 fsum2dlemstep 11235 fisumcom2 11239 fsumshftm 11246 fsumiun 11278 |
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