Theorem exbii

Description: Inference adding existential quantifier to both sides of an equivalence. (Contributed by NM, 24-May-1994)

	Ref	Expression
Hypothesis	exbii.1	$$⊢\phi \leftrightarrow \psi$$
Assertion	exbii	$$⊢\exists x\phi \leftrightarrow \exists x\psi$$

Proof

Step	Hyp	Ref	Expression
1		exbii.1	$$⊢\phi \leftrightarrow \psi$$
2		exbi	$$⊢\forall x\left(\phi \leftrightarrow \psi \right)\to \left(\exists x\phi \leftrightarrow \exists x\psi \right)$$
3	2 1	mpg	$$⊢\exists x\phi \leftrightarrow \exists x\psi$$