Theorem 2albidv

Description: Formula-building rule for two universal quantifiers (deduction form). (Contributed by NM, 4-Mar-1997)

	Ref	Expression
Hypothesis	2albidv.1	$$⊢\phi \to \left(\psi \leftrightarrow \chi \right)$$
Assertion	2albidv	$$⊢\phi \to \left(\forall x\forall y\psi \leftrightarrow \forall x\forall y\chi \right)$$

Proof

Step	Hyp	Ref	Expression
1		2albidv.1	$$⊢\phi \to \left(\psi \leftrightarrow \chi \right)$$
2	1	albidv	$$⊢\phi \to \left(\forall y\psi \leftrightarrow \forall y\chi \right)$$
3	2	albidv	$$⊢\phi \to \left(\forall x\forall y\psi \leftrightarrow \forall x\forall y\chi \right)$$