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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 28784 | . 2 ⊢ ((𝐴 ∈ (𝔼‘𝑁) ∧ 𝐼 ∈ (1...𝑁)) → (𝐴‘𝐼) ∈ ℝ) | |
2 | 1 | recnd 11274 | 1 ⊢ ((𝐴 ∈ (𝔼‘𝑁) ∧ 𝐼 ∈ (1...𝑁)) → (𝐴‘𝐼) ∈ ℂ) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 394 ∈ wcel 2098 ‘cfv 6549 (class class class)co 7419 ℂcc 11138 1c1 11141 ...cfz 13519 𝔼cee 28771 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1789 ax-4 1803 ax-5 1905 ax-6 1963 ax-7 2003 ax-8 2100 ax-9 2108 ax-10 2129 ax-11 2146 ax-12 2166 ax-ext 2696 ax-sep 5300 ax-nul 5307 ax-pow 5365 ax-pr 5429 ax-un 7741 ax-cnex 11196 ax-resscn 11197 |
This theorem depends on definitions: df-bi 206 df-an 395 df-or 846 df-3an 1086 df-tru 1536 df-fal 1546 df-ex 1774 df-nf 1778 df-sb 2060 df-mo 2528 df-eu 2557 df-clab 2703 df-cleq 2717 df-clel 2802 df-nfc 2877 df-ne 2930 df-ral 3051 df-rex 3060 df-rab 3419 df-v 3463 df-sbc 3774 df-dif 3947 df-un 3949 df-in 3951 df-ss 3961 df-nul 4323 df-if 4531 df-pw 4606 df-sn 4631 df-pr 4633 df-op 4637 df-uni 4910 df-br 5150 df-opab 5212 df-mpt 5233 df-id 5576 df-xp 5684 df-rel 5685 df-cnv 5686 df-co 5687 df-dm 5688 df-rn 5689 df-res 5690 df-ima 5691 df-iota 6501 df-fun 6551 df-fn 6552 df-f 6553 df-fv 6557 df-ov 7422 df-oprab 7423 df-mpo 7424 df-map 8847 df-ee 28774 |
This theorem is referenced by: brbtwn2 28788 colinearalglem2 28790 colinearalg 28793 axcgrrflx 28797 axcgrid 28799 axsegconlem1 28800 ax5seglem1 28811 ax5seglem2 28812 ax5seglem4 28815 ax5seglem5 28816 ax5seglem6 28817 ax5seglem9 28820 axbtwnid 28822 axpasch 28824 axlowdimlem16 28840 axlowdimlem17 28841 axeuclidlem 28845 axeuclid 28846 axcontlem2 28848 axcontlem4 28850 axcontlem7 28853 axcontlem8 28854 |
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