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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 |
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Ref | Expression |
---|---|
sumeq1d |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sumeq1d.1 |
. 2
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2 | sumeq1 11334 |
. 2
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3 | 1, 2 | syl 14 |
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-in1 614 ax-in2 615 ax-io 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-ext 2159 |
This theorem depends on definitions: df-bi 117 df-dc 835 df-3an 980 df-tru 1356 df-nf 1461 df-sb 1763 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-ral 2460 df-rex 2461 df-v 2739 df-un 3133 df-in 3135 df-ss 3142 df-if 3535 df-sn 3597 df-pr 3598 df-op 3600 df-uni 3808 df-br 4001 df-opab 4062 df-mpt 4063 df-cnv 4630 df-dm 4632 df-rn 4633 df-res 4634 df-iota 5173 df-f 5215 df-f1 5216 df-fo 5217 df-f1o 5218 df-fv 5219 df-ov 5871 df-oprab 5872 df-mpo 5873 df-recs 6299 df-frec 6385 df-seqfrec 10419 df-sumdc 11333 |
This theorem is referenced by: sumeq12dv 11351 sumeq12rdv 11352 fsumf1o 11369 fisumss 11371 fsumcllem 11378 fsum1 11391 fzosump1 11396 fsump1 11399 fsum2d 11414 fisumcom2 11417 fsumshftm 11424 fisumrev2 11425 telfsumo 11445 telfsum 11447 telfsum2 11448 fsumparts 11449 fsumiun 11456 bcxmas 11468 isumsplit 11470 isum1p 11471 arisum 11477 arisum2 11478 geoserap 11486 geolim 11490 geo2sum2 11494 cvgratnnlemseq 11505 cvgratnnlemsumlt 11507 mertenslemub 11513 mertenslemi1 11514 mertenslem2 11515 mertensabs 11516 efcvgfsum 11646 eftlub 11669 effsumlt 11671 eirraplem 11755 pcfac 12318 cvgcmp2nlemabs 14403 trilpolemeq1 14411 nconstwlpolemgt0 14434 |
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