Theorem exbi

Description: Theorem 19.18 of Margaris p. 90. (Contributed by NM, 12-Mar-1993)

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

Proof

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