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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 9186 | . 2 ⊢ (𝑥 ∈ ℤ → 𝑥 ∈ ℝ) | |
2 | 1 | ssriv 3141 | 1 ⊢ ℤ ⊆ ℝ |
Colors of variables: wff set class |
Syntax hints: ⊆ wss 3111 ℝcr 7743 ℤcz 9182 |
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 699 ax-5 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-10 1492 ax-11 1493 ax-i12 1494 ax-bndl 1496 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-ext 2146 |
This theorem depends on definitions: df-bi 116 df-3or 968 df-3an 969 df-tru 1345 df-nf 1448 df-sb 1750 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-rex 2448 df-rab 2451 df-v 2723 df-un 3115 df-in 3117 df-ss 3124 df-sn 3576 df-pr 3577 df-op 3579 df-uni 3784 df-br 3977 df-iota 5147 df-fv 5190 df-ov 5839 df-neg 8063 df-z 9183 |
This theorem is referenced by: suprzclex 9280 zred 9304 lbzbi 9545 fzval2 9938 seq3coll 10741 summodclem2a 11308 fsum3cvg3 11323 prodmodclem2a 11503 zsupcl 11865 infssuzex 11867 infssuzcldc 11869 gcddvds 11881 dvdslegcd 11882 |
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