Theorem stdpc5t

Description: Closed form of stdpc5 . (Possible to place it before 19.21t and use it to prove 19.21t ). (Contributed by BJ, 15-Sep-2018) (Proof modification is discouraged.)

	Ref	Expression
Assertion	stdpc5t	$$⊢Ⅎx\phi \to \left(\forall x\left(\phi \to \psi \right)\to \left(\phi \to \forall x\psi \right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		nf5r	$$⊢Ⅎx\phi \to \left(\phi \to \forall x\phi \right)$$
2		alim	$$⊢\forall x\left(\phi \to \psi \right)\to \left(\forall x\phi \to \forall x\psi \right)$$
3	1 2	syl9	$$⊢Ⅎx\phi \to \left(\forall x\left(\phi \to \psi \right)\to \left(\phi \to \forall x\psi \right)\right)$$