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Mirrors > Home > ILE Home > Th. List > zsscn | 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 9312 | . 2 ⊢ (𝑥 ∈ ℤ → 𝑥 ∈ ℂ) | |
2 | 1 | ssriv 3183 | 1 ⊢ ℤ ⊆ ℂ |
Colors of variables: wff set class |
Syntax hints: ⊆ wss 3153 ℂcc 7860 ℤcz 9307 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-io 710 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-10 1516 ax-11 1517 ax-i12 1518 ax-bndl 1520 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-ext 2175 ax-resscn 7954 |
This theorem depends on definitions: df-bi 117 df-3or 981 df-3an 982 df-tru 1367 df-nf 1472 df-sb 1774 df-clab 2180 df-cleq 2186 df-clel 2189 df-nfc 2325 df-rex 2478 df-rab 2481 df-v 2762 df-un 3157 df-in 3159 df-ss 3166 df-sn 3624 df-pr 3625 df-op 3627 df-uni 3836 df-br 4030 df-iota 5207 df-fv 5254 df-ov 5913 df-neg 8183 df-z 9308 |
This theorem is referenced by: zex 9316 divfnzn 9676 zexpcl 10612 fsumzcl 11532 fprodzcl 11739 4sqlem11 12526 zringbas 14056 zring0 14060 lmbrf 14354 lmres 14387 lgsfcl2 15064 2sqlem6 15145 |
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