Theorem rr2sscn2 45552

Description: The cartesian square of ℝ is a subset of the cartesian square of ℂ. (Contributed by Glauco Siliprandi, 3-Mar-2021.)

Assertion

Ref	Expression
rr2sscn2	⊢ (ℝ × ℝ) ⊆ (ℂ × ℂ)

Proof of Theorem rr2sscn2

Step	Hyp	Ref	Expression
1		ax-resscn 11081	. 2 ⊢ ℝ ⊆ ℂ
2		xpss12 5637	. 2 ⊢ ((ℝ ⊆ ℂ ∧ ℝ ⊆ ℂ) → (ℝ × ℝ) ⊆ (ℂ × ℂ))
3	1, 1, 2	mp2an 692	1 ⊢ (ℝ × ℝ) ⊆ (ℂ × ℂ)

Syntax hints:   ⊆ wss 3899   × cxp 5620  ℂcc 11022  ℝcr 11023

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1911  ax-6 1968  ax-7 2009  ax-8 2115  ax-9 2123  ax-ext 2706  ax-resscn 11081

This theorem depends on definitions:  df-bi 207  df-an 396  df-ex 1781  df-sb 2068  df-clab 2713  df-cleq 2726  df-clel 2809  df-ss 3916  df-opab 5159  df-xp 5628

This theorem is referenced by:  ovolval2lem  46829  ovolval2  46830  ovolval3  46833