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Mirrors > Home > MPE Home > Th. List > Mathboxes > zssxr | Structured version Visualization version GIF version |
Description: The integers are a subset of the extended reals. (Contributed by Glauco Siliprandi, 23-Oct-2021.) |
Ref | Expression |
---|---|
zssxr | ⊢ ℤ ⊆ ℝ* |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | zssre 11991 | . 2 ⊢ ℤ ⊆ ℝ | |
2 | ressxr 10687 | . 2 ⊢ ℝ ⊆ ℝ* | |
3 | 1, 2 | sstri 3978 | 1 ⊢ ℤ ⊆ ℝ* |
Colors of variables: wff setvar class |
Syntax hints: ⊆ wss 3938 ℝcr 10538 ℝ*cxr 10676 ℤcz 11984 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1796 ax-4 1810 ax-5 1911 ax-6 1970 ax-7 2015 ax-8 2116 ax-9 2124 ax-10 2145 ax-11 2161 ax-12 2177 ax-ext 2795 |
This theorem depends on definitions: df-bi 209 df-an 399 df-or 844 df-3or 1084 df-3an 1085 df-tru 1540 df-ex 1781 df-nf 1785 df-sb 2070 df-clab 2802 df-cleq 2816 df-clel 2895 df-nfc 2965 df-rab 3149 df-v 3498 df-dif 3941 df-un 3943 df-in 3945 df-ss 3954 df-nul 4294 df-if 4470 df-sn 4570 df-pr 4572 df-op 4576 df-uni 4841 df-br 5069 df-iota 6316 df-fv 6365 df-ov 7161 df-xr 10681 df-neg 10875 df-z 11985 |
This theorem is referenced by: limsupequzlem 42010 |
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