Theorem bnj216

Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011) (New usage is discouraged.)

	Ref	Expression
Hypothesis	bnj216.1	$$⊢B\in \mathrm{V}$$
Assertion	bnj216	$$⊢A=\mathrm{suc}B\to B\in A$$

Proof

Step	Hyp	Ref	Expression
1		bnj216.1	$$⊢B\in \mathrm{V}$$
2	1	sucid	$$⊢B\in \mathrm{suc}B$$
3		eleq2	$$⊢A=\mathrm{suc}B\to \left(B\in A\leftrightarrow B\in \mathrm{suc}B\right)$$
4	2 3	mpbiri	$$⊢A=\mathrm{suc}B\to B\in A$$