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	$$⊢A\in \mathrm{V}$$
Assertion	sucid	$$⊢A\in \mathrm{suc}A$$

Proof

Step	Hyp	Ref	Expression
1		sucid.1	$$⊢A\in \mathrm{V}$$
2		sucidg	$$⊢A\in \mathrm{V}\to A\in \mathrm{suc}A$$
3	1 2	ax-mp	$$⊢A\in \mathrm{suc}A$$