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	$$⊢\left(ℝ\subseteq {ℝ}^{*}\wedge ℝ\subseteq {ℝ}^{*}\right)\to {ℝ}^2\subseteq {ℝ}^{*}\times {ℝ}^{*}$$
3	1 1 2	mp2an	$$⊢{ℝ}^2\subseteq {ℝ}^{*}\times {ℝ}^{*}$$