Theorem sspwd

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

	Ref	Expression
Hypothesis	sspwd.1	$$⊢\phi \to A\subseteq B$$
Assertion	sspwd	$$⊢\phi \to 𝒫A\subseteq 𝒫B$$

Proof

Step	Hyp	Ref	Expression
1		sspwd.1	$$⊢\phi \to A\subseteq B$$
2		sspw	$$⊢A\subseteq B\to 𝒫A\subseteq 𝒫B$$
3	1 2	syl	$$⊢\phi \to 𝒫A\subseteq 𝒫B$$