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Metamath Proof Explorer

Theorem pssexg

Description: The proper subset of a set is also a set. (Contributed by Steven Nguyen, 17-Jul-2022)

		Ref	Expression
	Assertion	pssexg	$⊢ (A \subset B \land B \in C) \to A \in V$

Step	Hyp	Ref	Expression
1		pssss	$⊢ A \subset B \to A \subseteq B$
2		ssexg	$⊢ (A \subseteq B \land B \in C) \to A \in V$
3	1 2	sylan	$⊢ (A \subset B \land B \in C) \to A \in V$