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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 11124 | . 2 | |
3 | 1, 2 | syl 14 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1331 csu 11122 |
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 603 ax-in2 604 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 2121 |
This theorem depends on definitions: df-bi 116 df-dc 820 df-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-ral 2421 df-rex 2422 df-v 2688 df-un 3075 df-in 3077 df-ss 3084 df-if 3475 df-sn 3533 df-pr 3534 df-op 3536 df-uni 3737 df-br 3930 df-opab 3990 df-mpt 3991 df-cnv 4547 df-dm 4549 df-rn 4550 df-res 4551 df-iota 5088 df-f 5127 df-f1 5128 df-fo 5129 df-f1o 5130 df-fv 5131 df-ov 5777 df-oprab 5778 df-mpo 5779 df-recs 6202 df-frec 6288 df-seqfrec 10219 df-sumdc 11123 |
This theorem is referenced by: sumeq12dv 11141 sumeq12rdv 11142 fsumf1o 11159 fisumss 11161 fsumcllem 11168 fsum1 11181 fzosump1 11186 fsump1 11189 fsum2d 11204 fisumcom2 11207 fsumshftm 11214 fisumrev2 11215 telfsumo 11235 telfsum 11237 telfsum2 11238 fsumparts 11239 fsumiun 11246 bcxmas 11258 isumsplit 11260 isum1p 11261 arisum 11267 arisum2 11268 geoserap 11276 geolim 11280 geo2sum2 11284 cvgratnnlemseq 11295 cvgratnnlemsumlt 11297 mertenslemub 11303 mertenslemi1 11304 mertenslem2 11305 mertensabs 11306 efcvgfsum 11373 eftlub 11396 effsumlt 11398 eirraplem 11483 cvgcmp2nlemabs 13227 trilpolemeq1 13233 |
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