Theorem 2ralbii

Description: Inference adding two restricted universal quantifiers to both sides of an equivalence. (Contributed by NM, 1-Aug-2004)

	Ref	Expression
Hypothesis	2ralbii.1	$$⊢\phi \leftrightarrow \psi$$
Assertion	2ralbii	$$⊢\forall x\in A\forall y\in B\phi \leftrightarrow \forall x\in A\forall y\in B\psi$$

Proof

Step	Hyp	Ref	Expression
1		2ralbii.1	$$⊢\phi \leftrightarrow \psi$$
2	1	ralbii	$$⊢\forall y\in B\phi \leftrightarrow \forall y\in B\psi$$
3	2	ralbii	$$⊢\forall x\in A\forall y\in B\phi \leftrightarrow \forall x\in A\forall y\in B\psi$$