Theorem sucid

Description: A set belongs to its successor. (Contributed by NM, 22-Jun-1994) (Proof shortened by Alan Sare, 18-Feb-2012) (Proof shortened by Scott Fenton, 20-Feb-2012)

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

Proof

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