| Mathbox for Glauco Siliprandi |
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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 12620 | . 2 ⊢ ℤ ⊆ ℝ | |
| 2 | ressxr 11305 | . 2 ⊢ ℝ ⊆ ℝ* | |
| 3 | 1, 2 | sstri 3993 | 1 ⊢ ℤ ⊆ ℝ* |
| Colors of variables: wff setvar class |
| Syntax hints: ⊆ wss 3951 ℝcr 11154 ℝ*cxr 11294 ℤcz 12613 |
| This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1795 ax-4 1809 ax-5 1910 ax-6 1967 ax-7 2007 ax-8 2110 ax-9 2118 ax-ext 2708 |
| This theorem depends on definitions: df-bi 207 df-an 396 df-or 849 df-3or 1088 df-3an 1089 df-tru 1543 df-fal 1553 df-ex 1780 df-sb 2065 df-clab 2715 df-cleq 2729 df-clel 2816 df-rab 3437 df-v 3482 df-dif 3954 df-un 3956 df-ss 3968 df-nul 4334 df-if 4526 df-sn 4627 df-pr 4629 df-op 4633 df-uni 4908 df-br 5144 df-iota 6514 df-fv 6569 df-ov 7434 df-xr 11299 df-neg 11495 df-z 12614 |
| This theorem is referenced by: limsupequzlem 45737 |
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