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Theorem eluzelcn 27691
Description: A member of a set of upper integers is a complex number. (Contributed by Glauco Siliprandi, 29-Jun-2017.)
Assertion
Ref Expression
eluzelcn  |-  ( N  e.  ( ZZ>= `  M
)  ->  N  e.  CC )

Proof of Theorem eluzelcn
StepHypRef Expression
1 eluzelre 10489 . 2  |-  ( N  e.  ( ZZ>= `  M
)  ->  N  e.  RR )
21recnd 9106 1  |-  ( N  e.  ( ZZ>= `  M
)  ->  N  e.  CC )
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 1725   ` cfv 5446   CCcc 8980   ZZ>=cuz 10480
This theorem is referenced by:  stoweidlem14  27730
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 2416  ax-sep 4322  ax-nul 4330  ax-pow 4369  ax-pr 4395  ax-cnex 9038  ax-resscn 9039
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 2284  df-mo 2285  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ne 2600  df-ral 2702  df-rex 2703  df-rab 2706  df-v 2950  df-sbc 3154  df-dif 3315  df-un 3317  df-in 3319  df-ss 3326  df-nul 3621  df-if 3732  df-pw 3793  df-sn 3812  df-pr 3813  df-op 3815  df-uni 4008  df-br 4205  df-opab 4259  df-mpt 4260  df-id 4490  df-xp 4876  df-rel 4877  df-cnv 4878  df-co 4879  df-dm 4880  df-rn 4881  df-res 4882  df-ima 4883  df-iota 5410  df-fun 5448  df-fn 5449  df-f 5450  df-fv 5454  df-ov 6076  df-neg 9286  df-z 10275  df-uz 10481
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