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Theorem fzssuz 11093
Description: A finite set of sequential integers is a subset of a set of upper integers. (Contributed by NM, 28-Oct-2005.)
Assertion
Ref Expression
fzssuz  |-  ( M ... N )  C_  ( ZZ>= `  M )

Proof of Theorem fzssuz
Dummy variable  k is distinct from all other variables.
StepHypRef Expression
1 elfzuz 11055 . 2  |-  ( k  e.  ( M ... N )  ->  k  e.  ( ZZ>= `  M )
)
21ssriv 3352 1  |-  ( M ... N )  C_  ( ZZ>= `  M )
Colors of variables: wff set class
Syntax hints:    C_ wss 3320   ` cfv 5454  (class class class)co 6081   ZZ>=cuz 10488   ...cfz 11043
This theorem is referenced by:  fzof  11137  ltwefz  11303  seqcoll2  11713  caubnd  12162  climsup  12463  summolem2a  12509  fsumss  12519  fsumsers  12522  isumclim3  12543  binomlem  12608  isprm3  13088  2prm  13095  prmreclem5  13288  4sqlem11  13323  vdwnnlem1  13363  gsumval3  15514  fzssnn  24147  esumpcvgval  24468  esumcvg  24476  ballotlemfc0  24750  ballotlemfcc  24751  ballotlemiex  24759  ballotlemsup  24762  ballotlemsdom  24769  ballotlemsima  24773  ballotlemrv2  24779  erdszelem4  24880  erdszelem8  24884  prodmolem2a  25260  fprodntriv  25268  fprodss  25274  fprodefsum  25298  iprodclim3  25313  volsupnfl  26251  sdclem2  26446  geomcau  26465  diophin  26831  irrapxlem1  26885  climinf  27708  fzossnn0  28124
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-13 1727  ax-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417  ax-sep 4330  ax-nul 4338  ax-pow 4377  ax-pr 4403  ax-un 4701  ax-cnex 9046  ax-resscn 9047
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3or 937  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-eu 2285  df-mo 2286  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ne 2601  df-ral 2710  df-rex 2711  df-rab 2714  df-v 2958  df-sbc 3162  df-csb 3252  df-dif 3323  df-un 3325  df-in 3327  df-ss 3334  df-nul 3629  df-if 3740  df-pw 3801  df-sn 3820  df-pr 3821  df-op 3823  df-uni 4016  df-iun 4095  df-br 4213  df-opab 4267  df-mpt 4268  df-id 4498  df-xp 4884  df-rel 4885  df-cnv 4886  df-co 4887  df-dm 4888  df-rn 4889  df-res 4890  df-ima 4891  df-iota 5418  df-fun 5456  df-fn 5457  df-f 5458  df-fv 5462  df-ov 6084  df-oprab 6085  df-mpt2 6086  df-1st 6349  df-2nd 6350  df-neg 9294  df-z 10283  df-uz 10489  df-fz 11044
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