Theorem rr2sscn2 45327

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 11179	. 2 ⊢ ℝ ⊆ ℂ
2		xpss12 5667	. 2 ⊢ ((ℝ ⊆ ℂ ∧ ℝ ⊆ ℂ) → (ℝ × ℝ) ⊆ (ℂ × ℂ))
3	1, 1, 2	mp2an 692	1 ⊢ (ℝ × ℝ) ⊆ (ℂ × ℂ)

Syntax hints:   ⊆ wss 3924   × cxp 5650  ℂcc 11120  ℝcr 11121

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1794  ax-4 1808  ax-5 1909  ax-6 1966  ax-7 2006  ax-8 2109  ax-9 2117  ax-ext 2706  ax-resscn 11179

This theorem depends on definitions:  df-bi 207  df-an 396  df-ex 1779  df-sb 2064  df-clab 2713  df-cleq 2726  df-clel 2808  df-ss 3941  df-opab 5180  df-xp 5658

This theorem is referenced by:  ovolval2lem  46608  ovolval2  46609  ovolval3  46612