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Mirrors > Home > MPE Home > Th. List > fveecn | Structured version Visualization version GIF version |
Description: The function value of a point is a complex. (Contributed by Scott Fenton, 10-Jun-2013.) |
Ref | Expression |
---|---|
fveecn | ⊢ ((𝐴 ∈ (𝔼‘𝑁) ∧ 𝐼 ∈ (1...𝑁)) → (𝐴‘𝐼) ∈ ℂ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | fveere 25826 | . 2 ⊢ ((𝐴 ∈ (𝔼‘𝑁) ∧ 𝐼 ∈ (1...𝑁)) → (𝐴‘𝐼) ∈ ℝ) | |
2 | 1 | recnd 10106 | 1 ⊢ ((𝐴 ∈ (𝔼‘𝑁) ∧ 𝐼 ∈ (1...𝑁)) → (𝐴‘𝐼) ∈ ℂ) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 383 ∈ wcel 2030 ‘cfv 5926 (class class class)co 6690 ℂcc 9972 1c1 9975 ...cfz 12364 𝔼cee 25813 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1762 ax-4 1777 ax-5 1879 ax-6 1945 ax-7 1981 ax-8 2032 ax-9 2039 ax-10 2059 ax-11 2074 ax-12 2087 ax-13 2282 ax-ext 2631 ax-sep 4814 ax-nul 4822 ax-pow 4873 ax-pr 4936 ax-un 6991 ax-cnex 10030 ax-resscn 10031 |
This theorem depends on definitions: df-bi 197 df-or 384 df-an 385 df-3an 1056 df-tru 1526 df-ex 1745 df-nf 1750 df-sb 1938 df-eu 2502 df-mo 2503 df-clab 2638 df-cleq 2644 df-clel 2647 df-nfc 2782 df-ral 2946 df-rex 2947 df-rab 2950 df-v 3233 df-sbc 3469 df-dif 3610 df-un 3612 df-in 3614 df-ss 3621 df-nul 3949 df-if 4120 df-pw 4193 df-sn 4211 df-pr 4213 df-op 4217 df-uni 4469 df-br 4686 df-opab 4746 df-mpt 4763 df-id 5053 df-xp 5149 df-rel 5150 df-cnv 5151 df-co 5152 df-dm 5153 df-rn 5154 df-iota 5889 df-fun 5928 df-fn 5929 df-f 5930 df-fv 5934 df-ov 6693 df-oprab 6694 df-mpt2 6695 df-map 7901 df-ee 25816 |
This theorem is referenced by: brbtwn2 25830 colinearalglem2 25832 colinearalg 25835 axcgrrflx 25839 axcgrid 25841 axsegconlem1 25842 ax5seglem1 25853 ax5seglem2 25854 ax5seglem4 25857 ax5seglem5 25858 ax5seglem6 25859 ax5seglem9 25862 axbtwnid 25864 axpasch 25866 axlowdimlem16 25882 axlowdimlem17 25883 axeuclidlem 25887 axeuclid 25888 axcontlem2 25890 axcontlem4 25892 axcontlem7 25895 axcontlem8 25896 |
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