Theorem bj-2exbi

Description: Closed form of 2exbii . (Contributed by BJ, 6-May-2019)

	Ref	Expression
Assertion	bj-2exbi	$$⊢\forall x\forall y\left(\phi \leftrightarrow \psi \right)\to \left(\exists x\exists y\phi \leftrightarrow \exists x\exists y\psi \right)$$

Proof

Step	Hyp	Ref	Expression
1		exbi	$$⊢\forall y\left(\phi \leftrightarrow \psi \right)\to \left(\exists y\phi \leftrightarrow \exists y\psi \right)$$
2	1	alexbii	$$⊢\forall x\forall y\left(\phi \leftrightarrow \psi \right)\to \left(\exists x\exists y\phi \leftrightarrow \exists x\exists y\psi \right)$$