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Metamath Proof Explorer

Theorem prcssprc

Description: The superclass of a proper class is a proper class. (Contributed by AV, 27-Dec-2020)

		Ref	Expression
	Assertion	prcssprc	$⊢ (A \subseteq B \land A \notin V) \to B \notin V$

Step	Hyp	Ref	Expression
1		ssexg	$⊢ (A \subseteq B \land B \in V) \to A \in V$
2	1	ex	$⊢ A \subseteq B \to (B \in V \to A \in V)$
3	2	nelcon3d	$⊢ A \subseteq B \to (A \notin V \to B \notin V)$
4	3	imp	$⊢ (A \subseteq B \land A \notin V) \to B \notin V$