Metamath Proof Explorer


Theorem sspwi

Description: The powerclass preserves inclusion (inference form). (Contributed by BJ, 13-Apr-2024)

Ref Expression
Hypothesis sspwi.1 ⊢ A ⊆ B
Assertion sspwi ⊢ 𝒫 A ⊆ 𝒫 B

Proof

Step Hyp Ref Expression
1 sspwi.1 ⊢ A ⊆ B
2 sspw ⊢ A ⊆ B → 𝒫 A ⊆ 𝒫 B
3 1 2 ax-mp ⊢ 𝒫 A ⊆ 𝒫 B