Theorem rr2sscn2 46513

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 11264	. 2 ⊢ ℝ ⊆ ℂ
2		xpss12 5666	. 2 ⊢ ((ℝ ⊆ ℂ ∧ ℝ ⊆ ℂ) → (ℝ × ℝ) ⊆ (ℂ × ℂ))
3	1, 1, 2	mp2an 705	1 ⊢ (ℝ × ℝ) ⊆ (ℂ × ℂ)

This proof depends on syntax axioms:   ⊆ wss 3896   × cxp 5649  ℂcc 11205  ℝcr 11206

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1827  ax-4 1841  ax-5 1942  ax-6 1999  ax-7 2040  ax-8 2146  ax-9 2154  ax-ext 2732  ax-resscn 11264

This proof depends on definitions:  df-bi 210  df-an 402  df-ex 1812  df-sb 2099  df-clab 2739  df-cleq 2752  df-clel 2835  df-ss 3897  df-opab 5167  df-xp 5657

This theorem is used by:  ovolval2lem  47789  ovolval2  47790  ovolval3  47793