Theorem sspwd

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 )

Proof

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 )