Description: n-dimensional Lebesgue measurable sets are subsets of the n-dimensional real Euclidean space. (Contributed by Glauco Siliprandi, 3-Mar-2021)
Ref | Expression | ||
---|---|---|---|
Hypotheses | vonmblss2.x | ⊢ ( 𝜑 → 𝑋 ∈ Fin ) | |
vonmblss2.y | ⊢ ( 𝜑 → 𝑌 ∈ dom ( voln ‘ 𝑋 ) ) | ||
Assertion | vonmblss2 | ⊢ ( 𝜑 → 𝑌 ⊆ ( ℝ ↑m 𝑋 ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | vonmblss2.x | ⊢ ( 𝜑 → 𝑋 ∈ Fin ) | |
2 | vonmblss2.y | ⊢ ( 𝜑 → 𝑌 ∈ dom ( voln ‘ 𝑋 ) ) | |
3 | 1 | vonmblss | ⊢ ( 𝜑 → dom ( voln ‘ 𝑋 ) ⊆ 𝒫 ( ℝ ↑m 𝑋 ) ) |
4 | 3 2 | sseldd | ⊢ ( 𝜑 → 𝑌 ∈ 𝒫 ( ℝ ↑m 𝑋 ) ) |
5 | elpwi | ⊢ ( 𝑌 ∈ 𝒫 ( ℝ ↑m 𝑋 ) → 𝑌 ⊆ ( ℝ ↑m 𝑋 ) ) | |
6 | 4 5 | syl | ⊢ ( 𝜑 → 𝑌 ⊆ ( ℝ ↑m 𝑋 ) ) |