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 e. _V
Assertion	sucid	|- A e. suc A

Proof

Step	Hyp	Ref	Expression
1		sucid.1	|- A e. _V
2		sucidg	|- ( A e. _V -> A e. suc A )
3	1 2	ax-mp	|- A e. suc A