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Metamath Proof Explorer

Theorem ssd

Description: A sufficient condition for a subclass relationship. (Contributed by Glauco Siliprandi, 3-Jan-2021)

		Ref	Expression
	Hypothesis	ssd.1	$⊢ (φ \land x \in A) \to x \in B$
	Assertion	ssd	$⊢ φ \to A \subseteq B$

Step	Hyp	Ref	Expression
1		ssd.1	$⊢ (φ \land x \in A) \to x \in B$
2		nfv	$⊢ Ⅎ x φ$
3	2 1	ssdf	$⊢ φ \to A \subseteq B$