| Mathbox for Glauco Siliprandi |
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| Mirrors > Home > MPE Home > Th. List > Mathboxes > ssrexr | Structured version Visualization version GIF version | ||
| Description: A subset of the reals is a subset of the extended reals. (Contributed by Glauco Siliprandi, 2-Jan-2022.) |
| Ref | Expression |
|---|---|
| ssrexr.1 | ⊢ (𝜑 → 𝐴 ⊆ ℝ) |
| Ref | Expression |
|---|---|
| ssrexr | ⊢ (𝜑 → 𝐴 ⊆ ℝ*) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | ssrexr.1 | . 2 ⊢ (𝜑 → 𝐴 ⊆ ℝ) | |
| 2 | ressxr 11305 | . 2 ⊢ ℝ ⊆ ℝ* | |
| 3 | 1, 2 | sstrdi 3996 | 1 ⊢ (𝜑 → 𝐴 ⊆ ℝ*) |
| Colors of variables: wff setvar class |
| Syntax hints: → wi 4 ⊆ wss 3951 ℝcr 11154 ℝ*cxr 11294 |
| 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-tru 1543 df-ex 1780 df-sb 2065 df-clab 2715 df-cleq 2729 df-clel 2816 df-v 3482 df-un 3956 df-ss 3968 df-xr 11299 |
| This theorem is referenced by: limsuppnfdlem 45716 limsupvaluz2 45753 liminfval2 45783 |
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