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 × ℝ ) ⊆ ( ℝ* × ℝ* )

Proof

Step	Hyp	Ref	Expression
1		ressxr	⊢ ℝ ⊆ ℝ*
2		xpss12	⊢ ( ( ℝ ⊆ ℝ* ∧ ℝ ⊆ ℝ* ) → ( ℝ × ℝ ) ⊆ ( ℝ* × ℝ* ) )
3	1 1 2	mp2an	⊢ ( ℝ × ℝ ) ⊆ ( ℝ* × ℝ* )