Theorem albii

Description: Inference adding universal quantifier to both sides of an equivalence. (Contributed by NM, 7-Aug-1994)

	Ref	Expression
Hypothesis	albii.1	$$⊢\phi \leftrightarrow \psi$$
Assertion	albii	$$⊢\forall x\phi \leftrightarrow \forall x\psi$$

Proof

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