Theorem sucex

Description: The successor of a set is a set. (Contributed by NM, 30-Aug-1993)

	Ref	Expression
Hypothesis	sucex.1	⊢ 𝐴 ∈ V
Assertion	sucex	⊢ suc 𝐴 ∈ V

Proof

Step	Hyp	Ref	Expression
1		sucex.1	⊢ 𝐴 ∈ V
2		sucexg	⊢ ( 𝐴 ∈ V → suc 𝐴 ∈ V )
3	1 2	ax-mp	⊢ suc 𝐴 ∈ V