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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 |
---|---|
sumeq2dv |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sumeq2dv.1 |
. . 3
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2 | 1 | ralrimiva 2446 |
. 2
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3 | 2 | sumeq2d 10752 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-in1 579 ax-in2 580 ax-io 665 ax-5 1381 ax-7 1382 ax-gen 1383 ax-ie1 1427 ax-ie2 1428 ax-8 1440 ax-10 1441 ax-11 1442 ax-i12 1443 ax-bndl 1444 ax-4 1445 ax-13 1449 ax-14 1450 ax-17 1464 ax-i9 1468 ax-ial 1472 ax-i5r 1473 ax-ext 2070 ax-sep 3957 ax-pow 4009 ax-pr 4036 ax-un 4260 ax-setind 4353 ax-cnex 7434 ax-resscn 7435 ax-1cn 7436 ax-1re 7437 ax-icn 7438 ax-addcl 7439 ax-addrcl 7440 ax-mulcl 7441 ax-addcom 7443 ax-addass 7445 ax-distr 7447 ax-i2m1 7448 ax-0lt1 7449 ax-0id 7451 ax-rnegex 7452 ax-cnre 7454 ax-pre-ltirr 7455 ax-pre-ltwlin 7456 ax-pre-lttrn 7457 ax-pre-ltadd 7459 |
This theorem depends on definitions: df-bi 115 df-dc 781 df-3or 925 df-3an 926 df-tru 1292 df-fal 1295 df-nf 1395 df-sb 1693 df-eu 1951 df-mo 1952 df-clab 2075 df-cleq 2081 df-clel 2084 df-nfc 2217 df-ne 2256 df-nel 2351 df-ral 2364 df-rex 2365 df-reu 2366 df-rab 2368 df-v 2621 df-sbc 2841 df-csb 2934 df-dif 3001 df-un 3003 df-in 3005 df-ss 3012 df-if 3394 df-pw 3431 df-sn 3452 df-pr 3453 df-op 3455 df-uni 3654 df-int 3689 df-br 3846 df-opab 3900 df-mpt 3901 df-id 4120 df-xp 4444 df-rel 4445 df-cnv 4446 df-co 4447 df-dm 4448 df-rn 4449 df-res 4450 df-ima 4451 df-iota 4980 df-fun 5017 df-fn 5018 df-f 5019 df-f1 5020 df-f1o 5022 df-fv 5023 df-riota 5608 df-ov 5655 df-oprab 5656 df-mpt2 5657 df-recs 6070 df-frec 6156 df-pnf 7522 df-mnf 7523 df-xr 7524 df-ltxr 7525 df-le 7526 df-sub 7653 df-neg 7654 df-inn 8421 df-n0 8672 df-z 8749 df-uz 9018 df-fz 9423 df-iseq 9849 df-isum 10739 |
This theorem is referenced by: sumeq2sdv 10755 2sumeq2dv 10756 sumeq12dv 10757 sumeq12rdv 10758 sumfct 10759 fsumf1o 10778 fisumss 10780 fsumsplit 10797 isummulc1 10817 isumdivapc 10818 isumge0 10820 sumsplitdc 10822 fsum2dlemstep 10824 fsumshftm 10835 fisum0diag2 10837 fsummulc1 10839 fsumdivapc 10840 fsumneg 10841 fsumsub 10842 fsum2mul 10843 telfsumo2 10857 fsumparts 10860 hashiun 10868 hash2iun 10869 hash2iun1dif1 10870 binomlem 10873 binom1p 10875 isum1p 10882 arisum 10888 trireciplem 10890 geosergap 10896 geo2sum 10904 mertenslemi1 10925 mertenslem2 10926 mertensabs 10927 efval2 10951 efaddlem 10960 |
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