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Theorem rr2sscn2 45315
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 11209 . 2 ℝ ⊆ ℂ
2 xpss12 5703 . 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 3962   × cxp 5686  cc 11150  cr 11151
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1791  ax-4 1805  ax-5 1907  ax-6 1964  ax-7 2004  ax-8 2107  ax-9 2115  ax-ext 2705  ax-resscn 11209
This theorem depends on definitions:  df-bi 207  df-an 396  df-ex 1776  df-sb 2062  df-clab 2712  df-cleq 2726  df-clel 2813  df-ss 3979  df-opab 5210  df-xp 5694
This theorem is referenced by:  ovolval2lem  46598  ovolval2  46599  ovolval3  46602
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