Theorem hbal

Description: If x is not free in ph , it is not free in A. y ph . (Contributed by NM, 12-Mar-1993)

	Ref	Expression
Hypothesis	hbal.1	$$⊢\phi \to \forall x\phi$$
Assertion	hbal	$$⊢\forall y\phi \to \forall x\forall y\phi$$

Proof

Step	Hyp	Ref	Expression
1		hbal.1	$$⊢\phi \to \forall x\phi$$
2	1	alimi	$$⊢\forall y\phi \to \forall y\forall x\phi$$
3		ax-11	$$⊢\forall y\forall x\phi \to \forall x\forall y\phi$$
4	2 3	syl	$$⊢\forall y\phi \to \forall x\forall y\phi$$