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Theorem rr2sscn2 44155
Description: The cartesian square of is a subset of the cartesian square of . (Contributed by Glauco Siliprandi, 3-Mar-2021.)
Assertion
Ref Expression
rr2sscn2 (ℝ × ℝ) ⊆ (ℂ × ℂ)

Proof of Theorem rr2sscn2
StepHypRef Expression
1 ax-resscn 11169 . 2 ℝ ⊆ ℂ
2 xpss12 5691 . 2 ((ℝ ⊆ ℂ ∧ ℝ ⊆ ℂ) → (ℝ × ℝ) ⊆ (ℂ × ℂ))
31, 1, 2mp2an 690 1 (ℝ × ℝ) ⊆ (ℂ × ℂ)
Colors of variables: wff setvar class
Syntax hints:  wss 3948   × cxp 5674  cc 11110  cr 11111
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1913  ax-6 1971  ax-7 2011  ax-8 2108  ax-9 2116  ax-ext 2703  ax-resscn 11169
This theorem depends on definitions:  df-bi 206  df-an 397  df-tru 1544  df-ex 1782  df-sb 2068  df-clab 2710  df-cleq 2724  df-clel 2810  df-v 3476  df-in 3955  df-ss 3965  df-opab 5211  df-xp 5682
This theorem is referenced by:  ovolval2lem  45438  ovolval2  45439  ovolval3  45442
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