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Mirrors > Home > ILE Home > Th. List > sumeq2dv | Unicode version |
Description: Equality deduction for sum. (Contributed by NM, 3-Jan-2006.) (Revised by Mario Carneiro, 31-Jan-2014.) |
Ref | Expression |
---|---|
sumeq2dv.1 |
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Ref | Expression |
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sumeq2dv |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sumeq2dv.1 |
. . 3
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2 | 1 | ralrimiva 2563 |
. 2
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3 | 2 | sumeq2d 11410 |
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 615 ax-in2 616 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-13 2162 ax-14 2163 ax-ext 2171 ax-sep 4136 ax-pow 4192 ax-pr 4227 ax-un 4451 ax-setind 4554 ax-cnex 7933 ax-resscn 7934 ax-1cn 7935 ax-1re 7936 ax-icn 7937 ax-addcl 7938 ax-addrcl 7939 ax-mulcl 7940 ax-addcom 7942 ax-addass 7944 ax-distr 7946 ax-i2m1 7947 ax-0lt1 7948 ax-0id 7950 ax-rnegex 7951 ax-cnre 7953 ax-pre-ltirr 7954 ax-pre-ltwlin 7955 ax-pre-lttrn 7956 ax-pre-ltadd 7958 |
This theorem depends on definitions: df-bi 117 df-dc 836 df-3or 981 df-3an 982 df-tru 1367 df-fal 1370 df-nf 1472 df-sb 1774 df-eu 2041 df-mo 2042 df-clab 2176 df-cleq 2182 df-clel 2185 df-nfc 2321 df-ne 2361 df-nel 2456 df-ral 2473 df-rex 2474 df-reu 2475 df-rab 2477 df-v 2754 df-sbc 2978 df-csb 3073 df-dif 3146 df-un 3148 df-in 3150 df-ss 3157 df-if 3550 df-pw 3592 df-sn 3613 df-pr 3614 df-op 3616 df-uni 3825 df-int 3860 df-br 4019 df-opab 4080 df-mpt 4081 df-id 4311 df-xp 4650 df-rel 4651 df-cnv 4652 df-co 4653 df-dm 4654 df-rn 4655 df-res 4656 df-ima 4657 df-iota 5196 df-fun 5237 df-fn 5238 df-f 5239 df-f1 5240 df-f1o 5242 df-fv 5243 df-riota 5852 df-ov 5900 df-oprab 5901 df-mpo 5902 df-recs 6331 df-frec 6417 df-pnf 8025 df-mnf 8026 df-xr 8027 df-ltxr 8028 df-le 8029 df-sub 8161 df-neg 8162 df-inn 8951 df-n0 9208 df-z 9285 df-uz 9560 df-fz 10041 df-seqfrec 10479 df-sumdc 11397 |
This theorem is referenced by: sumeq2sdv 11413 2sumeq2dv 11414 sumeq12dv 11415 sumeq12rdv 11416 sumfct 11417 fsumf1o 11433 fisumss 11435 fsumsplit 11450 isummulc1 11470 isumdivapc 11471 isumge0 11473 sumsplitdc 11475 fsum2dlemstep 11477 fsumshftm 11488 fisum0diag2 11490 fsummulc1 11492 fsumdivapc 11493 fsumneg 11494 fsumsub 11495 fsum2mul 11496 telfsumo2 11510 fsumparts 11513 hashiun 11521 hash2iun 11522 hash2iun1dif1 11523 binomlem 11526 binom1p 11528 isum1p 11535 arisum 11541 trireciplem 11543 geosergap 11549 geo2sum 11557 mertenslemi1 11578 mertenslem2 11579 mertensabs 11580 efval2 11708 efaddlem 11717 phisum 12275 pcfac 12385 cvgcmp2nlemabs 15259 redcwlpolemeq1 15281 nconstwlpolem0 15290 |
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