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Theorem fveere 25088
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 25084 . 2  |-  ( A  e.  ( EE `  N )  ->  A : ( 1 ... N ) --> RR )
2 ffvelrn 5743 . 2  |-  ( ( A : ( 1 ... N ) --> RR 
/\  I  e.  ( 1 ... N ) )  ->  ( A `  I )  e.  RR )
31, 2sylan 457 1  |-  ( ( A  e.  ( EE
`  N )  /\  I  e.  ( 1 ... N ) )  ->  ( A `  I )  e.  RR )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 358    e. wcel 1710   -->wf 5330   ` cfv 5334  (class class class)co 5942   RRcr 8823   1c1 8825   ...cfz 10871   EEcee 25075
This theorem is referenced by:  fveecn  25089  eqeelen  25091  brbtwn2  25092  colinearalglem4  25096  colinearalg  25097  eleesub  25098  eleesubd  25099  axcgrid  25103  axsegconlem1  25104  axsegconlem2  25105  axsegconlem3  25106  axsegconlem8  25111  axsegconlem9  25112  axsegconlem10  25113  ax5seglem3a  25117  ax5seg  25125  axpasch  25128  axeuclidlem  25149  axcontlem2  25152
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-13 1712  ax-14 1714  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1930  ax-ext 2339  ax-sep 4220  ax-nul 4228  ax-pow 4267  ax-pr 4293  ax-un 4591  ax-cnex 8880  ax-resscn 8881
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-eu 2213  df-mo 2214  df-clab 2345  df-cleq 2351  df-clel 2354  df-nfc 2483  df-ne 2523  df-ral 2624  df-rex 2625  df-rab 2628  df-v 2866  df-sbc 3068  df-dif 3231  df-un 3233  df-in 3235  df-ss 3242  df-nul 3532  df-if 3642  df-pw 3703  df-sn 3722  df-pr 3723  df-op 3725  df-uni 3907  df-br 4103  df-opab 4157  df-mpt 4158  df-id 4388  df-xp 4774  df-rel 4775  df-cnv 4776  df-co 4777  df-dm 4778  df-rn 4779  df-iota 5298  df-fun 5336  df-fn 5337  df-f 5338  df-fv 5342  df-ov 5945  df-oprab 5946  df-mpt2 5947  df-map 6859  df-ee 25078
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