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Metamath Proof Explorer
Description: The cartesian square of RR is a subset of the cartesian square of
CC . (Contributed by Glauco Siliprandi, 3-Mar-2021)
|
|
Ref |
Expression |
|
Assertion |
rr2sscn2 |
⊢ ( ℝ × ℝ ) ⊆ ( ℂ × ℂ ) |
Proof
| Step |
Hyp |
Ref |
Expression |
| 1 |
|
ax-resscn |
⊢ ℝ ⊆ ℂ |
| 2 |
|
xpss12 |
⊢ ( ( ℝ ⊆ ℂ ∧ ℝ ⊆ ℂ ) → ( ℝ × ℝ ) ⊆ ( ℂ × ℂ ) ) |
| 3 |
1 1 2
|
mp2an |
⊢ ( ℝ × ℝ ) ⊆ ( ℂ × ℂ ) |