Theorem bj-elid3

Description: Characterization of the couples in _I whose first component is a setvar. (Contributed by BJ, 29-Mar-2020)

	Ref	Expression
Assertion	bj-elid3	⊢ ( ⟨ 𝑥 , 𝐴 ⟩ ∈ I ↔ 𝑥 = 𝐴 )

Proof

Step	Hyp	Ref	Expression
1		vex	⊢ 𝑥 ∈ V
2		bj-opelidb1	⊢ ( ⟨ 𝑥 , 𝐴 ⟩ ∈ I ↔ ( 𝑥 ∈ V ∧ 𝑥 = 𝐴 ) )
3	1 2	mpbiran	⊢ ( ⟨ 𝑥 , 𝐴 ⟩ ∈ I ↔ 𝑥 = 𝐴 )