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Theorem fveere 23152
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 23148 . 2  |-  ( A  e.  ( EE `  N )  ->  A : ( 1 ... N ) --> RR )
21ffvelrnda 5848 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 1756   ` cfv 5423  (class class class)co 6096   RRcr 9286   1c1 9288   ...cfz 11442   EEcee 23139
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1591  ax-4 1602  ax-5 1670  ax-6 1708  ax-7 1728  ax-8 1758  ax-9 1760  ax-10 1775  ax-11 1780  ax-12 1792  ax-13 1943  ax-ext 2423  ax-sep 4418  ax-nul 4426  ax-pow 4475  ax-pr 4536  ax-un 6377  ax-cnex 9343  ax-resscn 9344
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 967  df-tru 1372  df-ex 1587  df-nf 1590  df-sb 1701  df-eu 2257  df-mo 2258  df-clab 2430  df-cleq 2436  df-clel 2439  df-nfc 2573  df-ne 2613  df-ral 2725  df-rex 2726  df-rab 2729  df-v 2979  df-sbc 3192  df-dif 3336  df-un 3338  df-in 3340  df-ss 3347  df-nul 3643  df-if 3797  df-pw 3867  df-sn 3883  df-pr 3885  df-op 3889  df-uni 4097  df-br 4298  df-opab 4356  df-mpt 4357  df-id 4641  df-xp 4851  df-rel 4852  df-cnv 4853  df-co 4854  df-dm 4855  df-rn 4856  df-iota 5386  df-fun 5425  df-fn 5426  df-f 5427  df-fv 5431  df-ov 6099  df-oprab 6100  df-mpt2 6101  df-map 7221  df-ee 23142
This theorem is referenced by:  fveecn  23153  eqeelen  23155  brbtwn2  23156  colinearalglem4  23160  colinearalg  23161  eleesub  23162  eleesubd  23163  axcgrid  23167  axsegconlem1  23168  axsegconlem2  23169  axsegconlem3  23170  axsegconlem8  23175  axsegconlem9  23176  axsegconlem10  23177  ax5seglem3a  23181  ax5seg  23189  axpasch  23192  axeuclidlem  23213  axcontlem2  23216
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