Theorem ressxr

Description: The standard reals are a subset of the extended reals. (Contributed by NM, 14-Oct-2005)

	Ref	Expression
Assertion	ressxr	$$⊢ℝ\subseteq {ℝ}^{*}$$

Proof

Step	Hyp	Ref	Expression
1		ssun1	$$⊢ℝ\subseteq ℝ\cup \left\{\mathrm{+\infty },\mathrm{-\infty }\right\}$$
2		df-xr	$$⊢{ℝ}^{*}=ℝ\cup \left\{\mathrm{+\infty },\mathrm{-\infty }\right\}$$
3	1 2	sseqtrri	$$⊢ℝ\subseteq {ℝ}^{*}$$