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Mirrors > Home > ILE Home > Th. List > cvg1nlemf | Unicode version |
Description: Lemma for cvg1n 9585. The modified sequence is a sequence. (Contributed by Jim Kingdon, 1-Aug-2021.) |
Ref | Expression |
---|---|
cvg1n.f | |
cvg1n.c | |
cvg1n.cau | |
cvg1nlem.g | |
cvg1nlem.z | |
cvg1nlem.start |
Ref | Expression |
---|---|
cvg1nlemf |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cvg1n.f | . . . 4 | |
2 | 1 | adantr 261 | . . 3 |
3 | simpr 103 | . . . 4 | |
4 | cvg1nlem.z | . . . . 5 | |
5 | 4 | adantr 261 | . . . 4 |
6 | 3, 5 | nnmulcld 7962 | . . 3 |
7 | 2, 6 | ffvelrnd 5303 | . 2 |
8 | cvg1nlem.g | . 2 | |
9 | 7, 8 | fmptd 5322 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 wceq 1243 wcel 1393 wral 2306 class class class wbr 3764 cmpt 3818 wf 4898 cfv 4902 (class class class)co 5512 cr 6888 caddc 6892 cmul 6894 clt 7060 cdiv 7651 cn 7914 cuz 8473 crp 8583 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-14 1405 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 ax-sep 3875 ax-pow 3927 ax-pr 3944 ax-cnex 6975 ax-resscn 6976 ax-1cn 6977 ax-1re 6978 ax-icn 6979 ax-addcl 6980 ax-addrcl 6981 ax-mulcl 6982 ax-mulcom 6985 ax-addass 6986 ax-mulass 6987 ax-distr 6988 ax-1rid 6991 ax-cnre 6995 |
This theorem depends on definitions: df-bi 110 df-3an 887 df-tru 1246 df-nf 1350 df-sb 1646 df-eu 1903 df-mo 1904 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-ral 2311 df-rex 2312 df-rab 2315 df-v 2559 df-sbc 2765 df-un 2922 df-in 2924 df-ss 2931 df-pw 3361 df-sn 3381 df-pr 3382 df-op 3384 df-uni 3581 df-int 3616 df-br 3765 df-opab 3819 df-mpt 3820 df-id 4030 df-xp 4351 df-rel 4352 df-cnv 4353 df-co 4354 df-dm 4355 df-rn 4356 df-res 4357 df-ima 4358 df-iota 4867 df-fun 4904 df-fn 4905 df-f 4906 df-fv 4910 df-ov 5515 df-inn 7915 |
This theorem is referenced by: cvg1nlemres 9584 |
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