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Metamath Proof Explorer

Theorem sspwi

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

		Ref	Expression
	Hypothesis	sspwi.1	$⊢ A \subseteq B$
	Assertion	sspwi	$⊢ 𝒫 A \subseteq 𝒫 B$

Step	Hyp	Ref	Expression
1		sspwi.1	$⊢ A \subseteq B$
2		sspw	$⊢ A \subseteq B \to 𝒫 A \subseteq 𝒫 B$
3	1 2	ax-mp	$⊢ 𝒫 A \subseteq 𝒫 B$