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Theorem fveere 25845
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 25841 . 2  |-  ( A  e.  ( EE `  N )  ->  A : ( 1 ... N ) --> RR )
21ffvelrnda 5873 1  |-  ( ( A  e.  ( EE
`  N )  /\  I  e.  ( 1 ... N ) )  ->  ( A `  I )  e.  RR )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 360    e. wcel 1726   ` cfv 5457  (class class class)co 6084   RRcr 8994   1c1 8996   ...cfz 11048   EEcee 25832
This theorem is referenced by:  fveecn  25846  eqeelen  25848  brbtwn2  25849  colinearalglem4  25853  colinearalg  25854  eleesub  25855  eleesubd  25856  axcgrid  25860  axsegconlem1  25861  axsegconlem2  25862  axsegconlem3  25863  axsegconlem8  25868  axsegconlem9  25869  axsegconlem10  25870  ax5seglem3a  25874  ax5seg  25882  axpasch  25885  axeuclidlem  25906  axcontlem2  25909
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-13 1728  ax-14 1730  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419  ax-sep 4333  ax-nul 4341  ax-pow 4380  ax-pr 4406  ax-un 4704  ax-cnex 9051  ax-resscn 9052
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-eu 2287  df-mo 2288  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ne 2603  df-ral 2712  df-rex 2713  df-rab 2716  df-v 2960  df-sbc 3164  df-dif 3325  df-un 3327  df-in 3329  df-ss 3336  df-nul 3631  df-if 3742  df-pw 3803  df-sn 3822  df-pr 3823  df-op 3825  df-uni 4018  df-br 4216  df-opab 4270  df-mpt 4271  df-id 4501  df-xp 4887  df-rel 4888  df-cnv 4889  df-co 4890  df-dm 4891  df-rn 4892  df-iota 5421  df-fun 5459  df-fn 5460  df-f 5461  df-fv 5465  df-ov 6087  df-oprab 6088  df-mpt2 6089  df-map 7023  df-ee 25835
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