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Theorem fveere 24069
Description: The function value of a point is a real. (Contributed by Scott Fenton, 10-Jun-2013.)
Assertion
Ref Expression
fveere  |-  ( ( A  e.  ( EE
`  N )  /\  I  e.  ( 1 ... N ) )  ->  ( A `  I )  e.  RR )

Proof of Theorem fveere
StepHypRef Expression
1 eleei 24065 . 2  |-  ( A  e.  ( EE `  N )  ->  A : ( 1 ... N ) --> RR )
21ffvelrnda 6012 1  |-  ( ( A  e.  ( EE
`  N )  /\  I  e.  ( 1 ... N ) )  ->  ( A `  I )  e.  RR )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    /\ wa 369    e. wcel 1802   ` cfv 5574  (class class class)co 6277   RRcr 9489   1c1 9491   ...cfz 11676   EEcee 24056
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1603  ax-4 1616  ax-5 1689  ax-6 1732  ax-7 1774  ax-8 1804  ax-9 1806  ax-10 1821  ax-11 1826  ax-12 1838  ax-13 1983  ax-ext 2419  ax-sep 4554  ax-nul 4562  ax-pow 4611  ax-pr 4672  ax-un 6573  ax-cnex 9546  ax-resscn 9547
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 974  df-tru 1384  df-ex 1598  df-nf 1602  df-sb 1725  df-eu 2270  df-mo 2271  df-clab 2427  df-cleq 2433  df-clel 2436  df-nfc 2591  df-ne 2638  df-ral 2796  df-rex 2797  df-rab 2800  df-v 3095  df-sbc 3312  df-dif 3461  df-un 3463  df-in 3465  df-ss 3472  df-nul 3768  df-if 3923  df-pw 3995  df-sn 4011  df-pr 4013  df-op 4017  df-uni 4231  df-br 4434  df-opab 4492  df-mpt 4493  df-id 4781  df-xp 4991  df-rel 4992  df-cnv 4993  df-co 4994  df-dm 4995  df-rn 4996  df-iota 5537  df-fun 5576  df-fn 5577  df-f 5578  df-fv 5582  df-ov 6280  df-oprab 6281  df-mpt2 6282  df-map 7420  df-ee 24059
This theorem is referenced by:  fveecn  24070  eqeelen  24072  brbtwn2  24073  colinearalglem4  24077  colinearalg  24078  eleesub  24079  eleesubd  24080  axcgrid  24084  axsegconlem1  24085  axsegconlem2  24086  axsegconlem3  24087  axsegconlem8  24092  axsegconlem9  24093  axsegconlem10  24094  ax5seglem3a  24098  ax5seg  24106  axpasch  24109  axeuclidlem  24130  axcontlem2  24133
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