Theorem bj-alrim

Description: Closed form of alrimi . (Contributed by BJ, 2-May-2019)

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

Proof

Step	Hyp	Ref	Expression
1		nf5r	$$⊢Ⅎx\phi \to \left(\phi \to \forall x\phi \right)$$
2		sylgt	$$⊢\forall x\left(\phi \to \psi \right)\to \left(\left(\phi \to \forall x\phi \right)\to \left(\phi \to \forall x\psi \right)\right)$$
3	1 2	syl5com	$$⊢Ⅎx\phi \to \left(\forall x\left(\phi \to \psi \right)\to \left(\phi \to \forall x\psi \right)\right)$$