Theorem sylgt

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

	Ref	Expression
Assertion	sylgt	$$⊢\forall x\left(\psi \to \chi \right)\to \left(\left(\phi \to \forall x\psi \right)\to \left(\phi \to \forall x\chi \right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		alim	$$⊢\forall x\left(\psi \to \chi \right)\to \left(\forall x\psi \to \forall x\chi \right)$$
2	1	imim2d	$$⊢\forall x\left(\psi \to \chi \right)\to \left(\left(\phi \to \forall x\psi \right)\to \left(\phi \to \forall x\chi \right)\right)$$