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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 26250 | . 2 ⊢ ((𝐴 ∈ (𝔼‘𝑁) ∧ 𝐼 ∈ (1...𝑁)) → (𝐴‘𝐼) ∈ ℝ) | |
2 | 1 | recnd 10405 | 1 ⊢ ((𝐴 ∈ (𝔼‘𝑁) ∧ 𝐼 ∈ (1...𝑁)) → (𝐴‘𝐼) ∈ ℂ) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 386 ∈ wcel 2106 ‘cfv 6135 (class class class)co 6922 ℂcc 10270 1c1 10273 ...cfz 12643 𝔼cee 26237 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1839 ax-4 1853 ax-5 1953 ax-6 2021 ax-7 2054 ax-8 2108 ax-9 2115 ax-10 2134 ax-11 2149 ax-12 2162 ax-13 2333 ax-ext 2753 ax-sep 5017 ax-nul 5025 ax-pow 5077 ax-pr 5138 ax-un 7226 ax-cnex 10328 ax-resscn 10329 |
This theorem depends on definitions: df-bi 199 df-an 387 df-or 837 df-3an 1073 df-tru 1605 df-ex 1824 df-nf 1828 df-sb 2012 df-mo 2550 df-eu 2586 df-clab 2763 df-cleq 2769 df-clel 2773 df-nfc 2920 df-ral 3094 df-rex 3095 df-rab 3098 df-v 3399 df-sbc 3652 df-dif 3794 df-un 3796 df-in 3798 df-ss 3805 df-nul 4141 df-if 4307 df-pw 4380 df-sn 4398 df-pr 4400 df-op 4404 df-uni 4672 df-br 4887 df-opab 4949 df-mpt 4966 df-id 5261 df-xp 5361 df-rel 5362 df-cnv 5363 df-co 5364 df-dm 5365 df-rn 5366 df-iota 6099 df-fun 6137 df-fn 6138 df-f 6139 df-fv 6143 df-ov 6925 df-oprab 6926 df-mpt2 6927 df-map 8142 df-ee 26240 |
This theorem is referenced by: brbtwn2 26254 colinearalglem2 26256 colinearalg 26259 axcgrrflx 26263 axcgrid 26265 axsegconlem1 26266 ax5seglem1 26277 ax5seglem2 26278 ax5seglem4 26281 ax5seglem5 26282 ax5seglem6 26283 ax5seglem9 26286 axbtwnid 26288 axpasch 26290 axlowdimlem16 26306 axlowdimlem17 26307 axeuclidlem 26311 axeuclid 26312 axcontlem2 26314 axcontlem4 26316 axcontlem7 26319 axcontlem8 26320 |
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