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	$$⊢⟨x,A⟩\in \mathrm{I}\leftrightarrow x=A$$

Proof

Step	Hyp	Ref	Expression
1		vex	$$⊢x\in \mathrm{V}$$
2		bj-opelidb1	$$⊢⟨x,A⟩\in \mathrm{I}\leftrightarrow \left(x\in \mathrm{V}\wedge x=A\right)$$
3	1 2	mpbiran	$$⊢⟨x,A⟩\in \mathrm{I}\leftrightarrow x=A$$