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Metamath Proof Explorer

Theorem sucexg

Description: The successor of a set is a set (generalization). (Contributed by NM, 5-Jun-1994)

		Ref	Expression
	Assertion	sucexg	$⊢ A \in V \to suc A \in V$

Step	Hyp	Ref	Expression
1		elex	$⊢ A \in V \to A \in V$
2		sucexb	$⊢ A \in V \leftrightarrow suc A \in V$
3	1 2	sylib	$⊢ A \in V \to suc A \in V$