Theorem alrot4

Description: Rotate four universal quantifiers twice. (Contributed by NM, 2-Feb-2005) (Proof shortened by Fan Zheng, 6-Jun-2016)

	Ref	Expression
Assertion	alrot4	$$⊢\forall x\forall y\forall z\forall w\phi \leftrightarrow \forall z\forall w\forall x\forall y\phi$$

Proof

Step	Hyp	Ref	Expression
1		alrot3	$$⊢\forall y\forall z\forall w\phi \leftrightarrow \forall z\forall w\forall y\phi$$
2	1	albii	$$⊢\forall x\forall y\forall z\forall w\phi \leftrightarrow \forall x\forall z\forall w\forall y\phi$$
3		alrot3	$$⊢\forall x\forall z\forall w\forall y\phi \leftrightarrow \forall z\forall w\forall x\forall y\phi$$
4	2 3	bitri	$$⊢\forall x\forall y\forall z\forall w\phi \leftrightarrow \forall z\forall w\forall x\forall y\phi$$