Theorem bj-tagcg

Description: Characterization of the elements of B in terms of elements of its tagged version. (Contributed by BJ, 6-Oct-2018)

	Ref	Expression
Assertion	bj-tagcg	$$⊢A\in V\to \left(A\in B\leftrightarrow \left\{A\right\}\in tagB\right)$$

Proof

Step	Hyp	Ref	Expression
1		bj-snglc	$$⊢A\in B\leftrightarrow \left\{A\right\}\in snglB$$
2		bj-sngltag	$$⊢A\in V\to \left(\left\{A\right\}\in snglB\leftrightarrow \left\{A\right\}\in tagB\right)$$
3	1 2	syl5bb	$$⊢A\in V\to \left(A\in B\leftrightarrow \left\{A\right\}\in tagB\right)$$