Theorem rr2sscn2 38523

Description: ℝ^2 is a subset of CC^ 2. Common case. (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 9872	. 2 ⊢ ℝ ⊆ ℂ
2		xpss12 5148	. 2 ⊢ ((ℝ ⊆ ℂ ∧ ℝ ⊆ ℂ) → (ℝ × ℝ) ⊆ (ℂ × ℂ))
3	1, 1, 2	mp2an 704	1 ⊢ (ℝ × ℝ) ⊆ (ℂ × ℂ)

Syntax hints:   ⊆ wss 3540   × cxp 5036  ℂcc 9813  ℝcr 9814

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-10 2006  ax-11 2021  ax-12 2034  ax-13 2234  ax-ext 2590  ax-resscn 9872

This theorem depends on definitions:  df-bi 196  df-or 384  df-an 385  df-tru 1478  df-ex 1696  df-nf 1701  df-sb 1868  df-clab 2597  df-cleq 2603  df-clel 2606  df-nfc 2740  df-in 3547  df-ss 3554  df-opab 4644  df-xp 5044

This theorem is referenced by:  ovolval2lem  39533  ovolval2  39534  ovolval3  39537