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Mirrors > Home > MPE Home > Th. List > fzssz | Structured version Visualization version GIF version |
Description: A finite sequence of integers is a set of integers. (Contributed by Glauco Siliprandi, 11-Dec-2019.) |
Ref | Expression |
---|---|
fzssz | ⊢ (𝑀...𝑁) ⊆ ℤ |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elfzelz 12596 | . 2 ⊢ (𝑥 ∈ (𝑀...𝑁) → 𝑥 ∈ ℤ) | |
2 | 1 | ssriv 3802 | 1 ⊢ (𝑀...𝑁) ⊆ ℤ |
Colors of variables: wff setvar class |
Syntax hints: ⊆ wss 3769 (class class class)co 6878 ℤcz 11666 ...cfz 12580 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1891 ax-4 1905 ax-5 2006 ax-6 2072 ax-7 2107 ax-8 2159 ax-9 2166 ax-10 2185 ax-11 2200 ax-12 2213 ax-13 2377 ax-ext 2777 ax-sep 4975 ax-nul 4983 ax-pow 5035 ax-pr 5097 ax-un 7183 ax-cnex 10280 ax-resscn 10281 |
This theorem depends on definitions: df-bi 199 df-an 386 df-or 875 df-3or 1109 df-3an 1110 df-tru 1657 df-ex 1876 df-nf 1880 df-sb 2065 df-mo 2591 df-eu 2609 df-clab 2786 df-cleq 2792 df-clel 2795 df-nfc 2930 df-ne 2972 df-ral 3094 df-rex 3095 df-rab 3098 df-v 3387 df-sbc 3634 df-csb 3729 df-dif 3772 df-un 3774 df-in 3776 df-ss 3783 df-nul 4116 df-if 4278 df-pw 4351 df-sn 4369 df-pr 4371 df-op 4375 df-uni 4629 df-iun 4712 df-br 4844 df-opab 4906 df-mpt 4923 df-id 5220 df-xp 5318 df-rel 5319 df-cnv 5320 df-co 5321 df-dm 5322 df-rn 5323 df-res 5324 df-ima 5325 df-iota 6064 df-fun 6103 df-fn 6104 df-f 6105 df-fv 6109 df-ov 6881 df-oprab 6882 df-mpt2 6883 df-1st 7401 df-2nd 7402 df-neg 10559 df-z 11667 df-uz 11931 df-fz 12581 |
This theorem is referenced by: lcmflefac 15696 prmodvdslcmf 16084 prmolelcmf 16085 prmgaplcmlem1 16088 prmgaplcmlem2 16089 prmgaplcm 16097 fsum2dsub 31205 breprexplema 31228 breprexplemc 31230 breprexpnat 31232 vtsprod 31237 circlemeth 31238 fzisoeu 40259 fzsscn 40270 fzssre 40273 fzct 40340 fzossz 40343 sumnnodd 40606 dvnprodlem1 40905 dvnprodlem2 40906 fourierdlem20 41087 fourierdlem25 41092 fourierdlem37 41104 fourierdlem52 41118 fourierdlem64 41130 fourierdlem79 41145 etransclem32 41226 |
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