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Mirrors > Home > MPE Home > Th. List > cnelprrecn | Structured version Visualization version GIF version |
Description: Complex numbers are a subset of the pair of real and complex numbers (common case). (Contributed by David A. Wheeler, 8-Dec-2018.) |
Ref | Expression |
---|---|
cnelprrecn | ⊢ ℂ ∈ {ℝ, ℂ} |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cnex 9896 | . 2 ⊢ ℂ ∈ V | |
2 | 1 | prid2 4242 | 1 ⊢ ℂ ∈ {ℝ, ℂ} |
Colors of variables: wff setvar class |
Syntax hints: ∈ wcel 1977 {cpr 4127 ℂcc 9813 ℝcr 9814 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1713 ax-4 1728 ax-5 1827 ax-6 1875 ax-7 1922 ax-10 2006 ax-11 2021 ax-12 2034 ax-13 2234 ax-ext 2590 ax-cnex 9871 |
This theorem depends on definitions: df-bi 196 df-or 384 df-an 385 df-tru 1478 df-ex 1696 df-nf 1701 df-sb 1868 df-clab 2597 df-cleq 2603 df-clel 2606 df-nfc 2740 df-v 3175 df-un 3545 df-sn 4126 df-pr 4128 |
This theorem is referenced by: dvfcn 23478 dvnres 23500 dvexp 23522 dvexp3 23545 dvef 23547 dvsincos 23548 dvlipcn 23561 dv11cn 23568 dvply1 23843 dvtaylp 23928 pserdvlem2 23986 pige3 24073 dvlog 24197 advlogexp 24201 logtayl 24206 dvcxp1 24281 dvcxp2 24282 dvcncxp1 24284 dvatan 24462 efrlim 24496 lgamgulmlem2 24556 logdivsum 25022 log2sumbnd 25033 dvtan 32630 dvasin 32666 dvacos 32667 lhe4.4ex1a 37550 expgrowthi 37554 expgrowth 37556 binomcxplemdvbinom 37574 binomcxplemnotnn0 37577 dvsinexp 38798 dvrecg 38800 dvsinax 38801 dvasinbx 38810 dvcosax 38816 dvxpaek 38830 itgsincmulx 38866 fourierdlem56 39055 etransclem46 39173 |
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