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Mirrors > Home > ILE Home > Th. List > sumeq1i | Unicode version |
Description: Equality inference for sum. (Contributed by NM, 2-Jan-2006.) |
Ref | Expression |
---|---|
sumeq1i.1 |
Ref | Expression |
---|---|
sumeq1i |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sumeq1i.1 | . 2 | |
2 | sumeq1 11092 | . 2 | |
3 | 1, 2 | ax-mp 5 | 1 |
Colors of variables: wff set class |
Syntax hints: wceq 1316 csu 11090 |
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 588 ax-in2 589 ax-io 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 |
This theorem depends on definitions: df-bi 116 df-dc 805 df-3an 949 df-tru 1319 df-nf 1422 df-sb 1721 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-ral 2398 df-rex 2399 df-v 2662 df-un 3045 df-in 3047 df-ss 3054 df-if 3445 df-sn 3503 df-pr 3504 df-op 3506 df-uni 3707 df-br 3900 df-opab 3960 df-mpt 3961 df-cnv 4517 df-dm 4519 df-rn 4520 df-res 4521 df-iota 5058 df-f 5097 df-f1 5098 df-fo 5099 df-f1o 5100 df-fv 5101 df-ov 5745 df-oprab 5746 df-mpo 5747 df-recs 6170 df-frec 6256 df-seqfrec 10187 df-sumdc 11091 |
This theorem is referenced by: sumeq12i 11102 fsump1i 11170 fsum2d 11172 fsumxp 11173 isumnn0nn 11230 arisum 11235 arisum2 11236 geo2sum 11251 efsep 11324 ef4p 11327 dveflem 12782 |
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