![]() |
Mathbox for Glauco Siliprandi |
< Previous
Next >
Nearby theorems |
|
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 11289 | . 2 ⊢ ℝ ⊆ ℝ* | |
3 | 1, 2 | sstrdi 3992 | 1 ⊢ (𝜑 → 𝐴 ⊆ ℝ*) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ⊆ wss 3947 ℝcr 11138 ℝ*cxr 11278 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1790 ax-4 1804 ax-5 1906 ax-6 1964 ax-7 2004 ax-8 2101 ax-9 2109 ax-ext 2699 |
This theorem depends on definitions: df-bi 206 df-an 396 df-or 847 df-tru 1537 df-ex 1775 df-sb 2061 df-clab 2706 df-cleq 2720 df-clel 2806 df-v 3473 df-un 3952 df-in 3954 df-ss 3964 df-xr 11283 |
This theorem is referenced by: limsuppnfdlem 45089 liminfval2 45156 |
Copyright terms: Public domain | W3C validator |