Theorem bj-tagci

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-tagci	⊢ ( 𝐴 ∈ 𝐵 → { 𝐴 } ∈ tag 𝐵 )

Proof

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