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Theorem rr2sscn2 45377
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 11212 . 2 ℝ ⊆ ℂ
2 xpss12 5700 . 2 ((ℝ ⊆ ℂ ∧ ℝ ⊆ ℂ) → (ℝ × ℝ) ⊆ (ℂ × ℂ))
31, 1, 2mp2an 692 1 (ℝ × ℝ) ⊆ (ℂ × ℂ)
Colors of variables: wff setvar class
Syntax hints:  wss 3951   × cxp 5683  cc 11153  cr 11154
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-ext 2708  ax-resscn 11212
This theorem depends on definitions:  df-bi 207  df-an 396  df-ex 1780  df-sb 2065  df-clab 2715  df-cleq 2729  df-clel 2816  df-ss 3968  df-opab 5206  df-xp 5691
This theorem is referenced by:  ovolval2lem  46658  ovolval2  46659  ovolval3  46662
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