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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
StepHypRef Expression
1 ax-resscn 9872 . 2 ℝ ⊆ ℂ
2 xpss12 5148 . 2 ((ℝ ⊆ ℂ ∧ ℝ ⊆ ℂ) → (ℝ × ℝ) ⊆ (ℂ × ℂ))
31, 1, 2mp2an 704 1 (ℝ × ℝ) ⊆ (ℂ × ℂ)
 Colors of variables: wff setvar class 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
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