This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

Theorem ressxr

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

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

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