Theorem bj-stdpc5

Description: More direct proof of stdpc5 . (Contributed by BJ, 15-Sep-2018) (Proof modification is discouraged.)

	Ref	Expression
Hypothesis	bj-stdpc5.1	$$⊢Ⅎx\phi$$
Assertion	bj-stdpc5	$$⊢\forall x\left(\phi \to \psi \right)\to \left(\phi \to \forall x\psi \right)$$

Proof

Step	Hyp	Ref	Expression
1		bj-stdpc5.1	$$⊢Ⅎx\phi$$
2		stdpc5t	$$⊢Ⅎx\phi \to \left(\forall x\left(\phi \to \psi \right)\to \left(\phi \to \forall x\psi \right)\right)$$
3	1 2	ax-mp	$$⊢\forall x\left(\phi \to \psi \right)\to \left(\phi \to \forall x\psi \right)$$