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Theorem rr2sscn2 43248
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 11029 . 2 ℝ ⊆ ℂ
2 xpss12 5635 . 2 ((ℝ ⊆ ℂ ∧ ℝ ⊆ ℂ) → (ℝ × ℝ) ⊆ (ℂ × ℂ))
31, 1, 2mp2an 689 1 (ℝ × ℝ) ⊆ (ℂ × ℂ)
Colors of variables: wff setvar class
Syntax hints:  wss 3898   × cxp 5618  cc 10970  cr 10971
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1912  ax-6 1970  ax-7 2010  ax-8 2107  ax-9 2115  ax-ext 2707  ax-resscn 11029
This theorem depends on definitions:  df-bi 206  df-an 397  df-tru 1543  df-ex 1781  df-sb 2067  df-clab 2714  df-cleq 2728  df-clel 2814  df-v 3443  df-in 3905  df-ss 3915  df-opab 5155  df-xp 5626
This theorem is referenced by:  ovolval2lem  44526  ovolval2  44527  ovolval3  44530
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