Description: The powerclass preserves inclusion (deduction form). (Contributed by BJ, 13-Apr-2024)
Ref | Expression | ||
---|---|---|---|
Hypothesis | sspwd.1 | ⊢ ( 𝜑 → 𝐴 ⊆ 𝐵 ) | |
Assertion | sspwd | ⊢ ( 𝜑 → 𝒫 𝐴 ⊆ 𝒫 𝐵 ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sspwd.1 | ⊢ ( 𝜑 → 𝐴 ⊆ 𝐵 ) | |
2 | sspw | ⊢ ( 𝐴 ⊆ 𝐵 → 𝒫 𝐴 ⊆ 𝒫 𝐵 ) | |
3 | 1 2 | syl | ⊢ ( 𝜑 → 𝒫 𝐴 ⊆ 𝒫 𝐵 ) |