Theorem 3albii

Description: Inference adding three universal quantifiers to both sides of an equivalence. (Contributed by Peter Mazsa, 10-Aug-2018)

	Ref	Expression
Hypothesis	3albii.1	$$⊢\phi \leftrightarrow \psi$$
Assertion	3albii	$$⊢\forall x\forall y\forall z\phi \leftrightarrow \forall x\forall y\forall z\psi$$

Proof

Step	Hyp	Ref	Expression
1		3albii.1	$$⊢\phi \leftrightarrow \psi$$
2	1	2albii	$$⊢\forall y\forall z\phi \leftrightarrow \forall y\forall z\psi$$
3	2	albii	$$⊢\forall x\forall y\forall z\phi \leftrightarrow \forall x\forall y\forall z\psi$$