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Mirrors > Home > ILE Home > Th. List > cvg1nlemf | Unicode version |
Description: Lemma for cvg1n 10751. 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 274 | . . 3 |
3 | simpr 109 | . . . 4 | |
4 | cvg1nlem.z | . . . . 5 | |
5 | 4 | adantr 274 | . . . 4 |
6 | 3, 5 | nnmulcld 8762 | . . 3 |
7 | 2, 6 | ffvelrnd 5549 | . 2 |
8 | cvg1nlem.g | . 2 | |
9 | 7, 8 | fmptd 5567 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wceq 1331 wcel 1480 wral 2414 class class class wbr 3924 cmpt 3984 wf 5114 cfv 5118 (class class class)co 5767 cr 7612 caddc 7616 cmul 7618 clt 7793 cdiv 8425 cn 8713 cuz 9319 crp 9434 |
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-io 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-14 1492 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2119 ax-sep 4041 ax-pow 4093 ax-pr 4126 ax-cnex 7704 ax-resscn 7705 ax-1cn 7706 ax-1re 7707 ax-icn 7708 ax-addcl 7709 ax-addrcl 7710 ax-mulcl 7711 ax-mulcom 7714 ax-addass 7715 ax-mulass 7716 ax-distr 7717 ax-1rid 7720 ax-cnre 7724 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-eu 2000 df-mo 2001 df-clab 2124 df-cleq 2130 df-clel 2133 df-nfc 2268 df-ral 2419 df-rex 2420 df-rab 2423 df-v 2683 df-sbc 2905 df-un 3070 df-in 3072 df-ss 3079 df-pw 3507 df-sn 3528 df-pr 3529 df-op 3531 df-uni 3732 df-int 3767 df-br 3925 df-opab 3985 df-mpt 3986 df-id 4210 df-xp 4540 df-rel 4541 df-cnv 4542 df-co 4543 df-dm 4544 df-rn 4545 df-res 4546 df-ima 4547 df-iota 5083 df-fun 5120 df-fn 5121 df-f 5122 df-fv 5126 df-ov 5770 df-inn 8714 |
This theorem is referenced by: cvg1nlemres 10750 |
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