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Metamath Proof Explorer

Theorem rexpssxrxp

Description: The Cartesian product of standard reals are a subset of the Cartesian product of extended reals. (Contributed by David A. Wheeler, 8-Dec-2018)

		Ref	Expression
	Assertion	rexpssxrxp	$⊢ ℝ^{2} \subseteq ℝ^{} \times ℝ^{}$

Proof

Step	Hyp	Ref	Expression
1		ressxr	$⊢ ℝ \subseteq ℝ^{*}$
2		xpss12	$⊢ (ℝ \subseteq ℝ^{} \land ℝ \subseteq ℝ^{}) \to ℝ^{2} \subseteq ℝ^{} \times ℝ^{}$
3	1 1 2	mp2an	$⊢ ℝ^{2} \subseteq ℝ^{} \times ℝ^{}$