Theorem elsuc2

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

	Ref	Expression
Hypothesis	elsuc.1	$$⊢A\in \mathrm{V}$$
Assertion	elsuc2	$$⊢B\in \mathrm{suc}A\leftrightarrow \left(B\in A\vee B=A\right)$$

Proof

Step	Hyp	Ref	Expression
1		elsuc.1	$$⊢A\in \mathrm{V}$$
2		elsuc2g	$$⊢A\in \mathrm{V}\to \left(B\in \mathrm{suc}A\leftrightarrow \left(B\in A\vee B=A\right)\right)$$
3	1 2	ax-mp	$$⊢B\in \mathrm{suc}A\leftrightarrow \left(B\in A\vee B=A\right)$$