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Mirrors > Home > MPE Home > Th. List > zsscn | Structured version Visualization version GIF version |
Description: The integers are a subset of the complex numbers. (Contributed by NM, 2-Aug-2004.) |
Ref | Expression |
---|---|
zsscn | ⊢ ℤ ⊆ ℂ |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | zcn 11259 | . 2 ⊢ (𝑥 ∈ ℤ → 𝑥 ∈ ℂ) | |
2 | 1 | ssriv 3572 | 1 ⊢ ℤ ⊆ ℂ |
Colors of variables: wff setvar class |
Syntax hints: ⊆ wss 3540 ℂcc 9813 ℤcz 11254 |
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-resscn 9872 |
This theorem depends on definitions: df-bi 196 df-or 384 df-an 385 df-3or 1032 df-3an 1033 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-rex 2902 df-rab 2905 df-v 3175 df-dif 3543 df-un 3545 df-in 3547 df-ss 3554 df-nul 3875 df-if 4037 df-sn 4126 df-pr 4128 df-op 4132 df-uni 4373 df-br 4584 df-iota 5768 df-fv 5812 df-ov 6552 df-neg 10148 df-z 11255 |
This theorem is referenced by: zex 11263 elq 11666 zexpcl 12737 fsumzcl 14313 fprodzcl 14523 zrisefaccl 14590 zfallfaccl 14591 4sqlem11 15497 zringbas 19643 zring0 19647 lmbrf 20874 lmres 20914 sszcld 22428 lmmbrf 22868 iscauf 22886 caucfil 22889 lmclimf 22910 elqaalem3 23880 iaa 23884 aareccl 23885 wilthlem2 24595 wilthlem3 24596 lgsfcl2 24828 2sqlem6 24948 zringnm 29332 caures 32726 mzpexpmpt 36326 uzmptshftfval 37567 fzsscn 38467 dvnprodlem1 38836 dvnprodlem2 38837 elaa2lem 39126 oddibas 41603 2zrngbas 41726 2zrng0 41728 |
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