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 ∈ 𝑉 → ( 𝐴 ∈ 𝐵 ↔ { 𝐴 } ∈ tag 𝐵 ) )

Proof

Step	Hyp	Ref	Expression
1		bj-snglc	⊢ ( 𝐴 ∈ 𝐵 ↔ { 𝐴 } ∈ sngl 𝐵 )
2		bj-sngltag	⊢ ( 𝐴 ∈ 𝑉 → ( { 𝐴 } ∈ sngl 𝐵 ↔ { 𝐴 } ∈ tag 𝐵 ) )
3	1 2	bitrid	⊢ ( 𝐴 ∈ 𝑉 → ( 𝐴 ∈ 𝐵 ↔ { 𝐴 } ∈ tag 𝐵 ) )