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