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Metamath Proof Explorer

Theorem sspwd

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

		Ref	Expression
	Hypothesis	sspwd.1	$⊢ φ \to A \subseteq B$
	Assertion	sspwd	$⊢ φ \to 𝒫 A \subseteq 𝒫 B$

Step	Hyp	Ref	Expression
1		sspwd.1	$⊢ φ \to A \subseteq B$
2		sspw	$⊢ A \subseteq B \to 𝒫 A \subseteq 𝒫 B$
3	1 2	syl	$⊢ φ \to 𝒫 A \subseteq 𝒫 B$