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Mirrors > Home > ILE Home > Th. List > zssre | GIF version |
Description: The integers are a subset of the reals. (Contributed by NM, 2-Aug-2004.) |
Ref | Expression |
---|---|
zssre | ⊢ ℤ ⊆ ℝ |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | zre 9058 | . 2 ⊢ (𝑥 ∈ ℤ → 𝑥 ∈ ℝ) | |
2 | 1 | ssriv 3101 | 1 ⊢ ℤ ⊆ ℝ |
Colors of variables: wff set class |
Syntax hints: ⊆ wss 3071 ℝcr 7619 ℤcz 9054 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 |
This theorem depends on definitions: df-bi 116 df-3or 963 df-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-rex 2422 df-rab 2425 df-v 2688 df-un 3075 df-in 3077 df-ss 3084 df-sn 3533 df-pr 3534 df-op 3536 df-uni 3737 df-br 3930 df-iota 5088 df-fv 5131 df-ov 5777 df-neg 7936 df-z 9055 |
This theorem is referenced by: suprzclex 9149 zred 9173 lbzbi 9408 fzval2 9793 seq3coll 10585 summodclem2a 11150 fsum3cvg3 11165 prodmodclem2a 11345 zsupcl 11640 infssuzex 11642 infssuzcldc 11644 gcddvds 11652 dvdslegcd 11653 |
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