Theorem alrot3

Description: Theorem *11.21 in WhiteheadRussell p. 160. (Contributed by Andrew Salmon, 24-May-2011)

	Ref	Expression
Assertion	alrot3	$$⊢\forall x\forall y\forall z\phi \leftrightarrow \forall y\forall z\forall x\phi$$

Proof

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