Theorem rr2sscn2 44076

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 11167	. 2 ⊢ ℝ ⊆ ℂ
2		xpss12 5692	. 2 ⊢ ((ℝ ⊆ ℂ ∧ ℝ ⊆ ℂ) → (ℝ × ℝ) ⊆ (ℂ × ℂ))
3	1, 1, 2	mp2an 691	1 ⊢ (ℝ × ℝ) ⊆ (ℂ × ℂ)

Syntax hints:   ⊆ wss 3949   × cxp 5675  ℂcc 11108  ℝcr 11109

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2109  ax-9 2117  ax-ext 2704  ax-resscn 11167

This theorem depends on definitions:  df-bi 206  df-an 398  df-tru 1545  df-ex 1783  df-sb 2069  df-clab 2711  df-cleq 2725  df-clel 2811  df-v 3477  df-in 3956  df-ss 3966  df-opab 5212  df-xp 5683

This theorem is referenced by:  ovolval2lem  45359  ovolval2  45360  ovolval3  45363