Theorem elsuc2

Description: Membership in a successor. (Contributed by NM, 15-Sep-2003)

	Ref	Expression
Hypothesis	elsuc.1	|- A e. _V
Assertion	elsuc2	|- ( B e. suc A <-> ( B e. A \/ B = A ) )

Proof

Step	Hyp	Ref	Expression
1		elsuc.1	|- A e. _V
2		elsuc2g	|- ( A e. _V -> ( B e. suc A <-> ( B e. A \/ B = A ) ) )
3	1 2	ax-mp	|- ( B e. suc A <-> ( B e. A \/ B = A ) )