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Mirrors > Home > ILE Home > Th. List > sumeq1d | Unicode version |
Description: Equality deduction for sum. (Contributed by NM, 1-Nov-2005.) |
Ref | Expression |
---|---|
sumeq1d.1 |
Ref | Expression |
---|---|
sumeq1d |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sumeq1d.1 | . 2 | |
2 | sumeq1 11282 | . 2 | |
3 | 1, 2 | syl 14 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1342 csu 11280 |
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-in1 604 ax-in2 605 ax-io 699 ax-5 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-10 1492 ax-11 1493 ax-i12 1494 ax-bndl 1496 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-ext 2146 |
This theorem depends on definitions: df-bi 116 df-dc 825 df-3an 969 df-tru 1345 df-nf 1448 df-sb 1750 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-ral 2447 df-rex 2448 df-v 2723 df-un 3115 df-in 3117 df-ss 3124 df-if 3516 df-sn 3576 df-pr 3577 df-op 3579 df-uni 3784 df-br 3977 df-opab 4038 df-mpt 4039 df-cnv 4606 df-dm 4608 df-rn 4609 df-res 4610 df-iota 5147 df-f 5186 df-f1 5187 df-fo 5188 df-f1o 5189 df-fv 5190 df-ov 5839 df-oprab 5840 df-mpo 5841 df-recs 6264 df-frec 6350 df-seqfrec 10371 df-sumdc 11281 |
This theorem is referenced by: sumeq12dv 11299 sumeq12rdv 11300 fsumf1o 11317 fisumss 11319 fsumcllem 11326 fsum1 11339 fzosump1 11344 fsump1 11347 fsum2d 11362 fisumcom2 11365 fsumshftm 11372 fisumrev2 11373 telfsumo 11393 telfsum 11395 telfsum2 11396 fsumparts 11397 fsumiun 11404 bcxmas 11416 isumsplit 11418 isum1p 11419 arisum 11425 arisum2 11426 geoserap 11434 geolim 11438 geo2sum2 11442 cvgratnnlemseq 11453 cvgratnnlemsumlt 11455 mertenslemub 11461 mertenslemi1 11462 mertenslem2 11463 mertensabs 11464 efcvgfsum 11594 eftlub 11617 effsumlt 11619 eirraplem 11703 pcfac 12259 cvgcmp2nlemabs 13752 trilpolemeq1 13760 nconstwlpolemgt0 13783 |
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