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Theorem fveere 28424
Description: The function value of a point is a real. (Contributed by Scott Fenton, 10-Jun-2013.)
Assertion
Ref Expression
fveere ((𝐴 ∈ (π”Όβ€˜π‘) ∧ 𝐼 ∈ (1...𝑁)) β†’ (π΄β€˜πΌ) ∈ ℝ)

Proof of Theorem fveere
StepHypRef Expression
1 eleei 28420 . 2 (𝐴 ∈ (π”Όβ€˜π‘) β†’ 𝐴:(1...𝑁)βŸΆβ„)
21ffvelcdmda 7087 1 ((𝐴 ∈ (π”Όβ€˜π‘) ∧ 𝐼 ∈ (1...𝑁)) β†’ (π΄β€˜πΌ) ∈ ℝ)
Colors of variables: wff setvar class
Syntax hints:   β†’ wi 4   ∧ wa 394   ∈ wcel 2104  β€˜cfv 6544  (class class class)co 7413  β„cr 11113  1c1 11115  ...cfz 13490  π”Όcee 28411
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1911  ax-6 1969  ax-7 2009  ax-8 2106  ax-9 2114  ax-10 2135  ax-11 2152  ax-12 2169  ax-ext 2701  ax-sep 5300  ax-nul 5307  ax-pow 5364  ax-pr 5428  ax-un 7729  ax-cnex 11170  ax-resscn 11171
This theorem depends on definitions:  df-bi 206  df-an 395  df-or 844  df-3an 1087  df-tru 1542  df-fal 1552  df-ex 1780  df-nf 1784  df-sb 2066  df-mo 2532  df-eu 2561  df-clab 2708  df-cleq 2722  df-clel 2808  df-nfc 2883  df-ne 2939  df-ral 3060  df-rex 3069  df-rab 3431  df-v 3474  df-sbc 3779  df-dif 3952  df-un 3954  df-in 3956  df-ss 3966  df-nul 4324  df-if 4530  df-pw 4605  df-sn 4630  df-pr 4632  df-op 4636  df-uni 4910  df-br 5150  df-opab 5212  df-mpt 5233  df-id 5575  df-xp 5683  df-rel 5684  df-cnv 5685  df-co 5686  df-dm 5687  df-rn 5688  df-res 5689  df-ima 5690  df-iota 6496  df-fun 6546  df-fn 6547  df-f 6548  df-fv 6552  df-ov 7416  df-oprab 7417  df-mpo 7418  df-map 8826  df-ee 28414
This theorem is referenced by:  fveecn  28425  eqeelen  28427  brbtwn2  28428  colinearalglem4  28432  colinearalg  28433  eleesub  28434  eleesubd  28435  axcgrid  28439  axsegconlem1  28440  axsegconlem2  28441  axsegconlem3  28442  axsegconlem8  28447  axsegconlem9  28448  axsegconlem10  28449  ax5seglem3a  28453  ax5seg  28461  axpasch  28464  axeuclidlem  28485  axcontlem2  28488
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