Theorem bj-spst

Description: Closed form of sps . Once in main part, prove sps and spsd from it. (Contributed by BJ, 20-Oct-2019)

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

Proof

Step	Hyp	Ref	Expression
1		sp	$$⊢\forall x\phi \to \phi$$
2	1	imim1i	$$⊢\left(\phi \to \psi \right)\to \left(\forall x\phi \to \psi \right)$$