Theorem bj-bialal

Description: When ph is substituted for ps , both sides express a form of nonfreeness. (Contributed by BJ, 20-Oct-2019)

	Ref	Expression
Assertion	bj-bialal	$$⊢\forall x\left(\forall x\phi \to \psi \right)\leftrightarrow \left(\forall x\phi \to \forall x\psi \right)$$

Proof

Step	Hyp	Ref	Expression
1		nfa1	$$⊢Ⅎx\forall x\phi$$
2	1	19.21	$$⊢\forall x\left(\forall x\phi \to \psi \right)\leftrightarrow \left(\forall x\phi \to \forall x\psi \right)$$