Theorem stdpc5v

Description: Version of stdpc5 with a disjoint variable condition, requiring fewer axioms. (Contributed by BJ, 7-Mar-2020) Revised to shorten 19.21v . (Revised by Wolf Lammen, 12-Jul-2020)

	Ref	Expression
Assertion	stdpc5v	$$⊢\forall x\left(\phi \to \psi \right)\to \left(\phi \to \forall x\psi \right)$$

Proof

Step	Hyp	Ref	Expression
1		ax-5	$$⊢\phi \to \forall x\phi$$
2		alim	$$⊢\forall x\left(\phi \to \psi \right)\to \left(\forall x\phi \to \forall x\psi \right)$$
3	1 2	syl5	$$⊢\forall x\left(\phi \to \psi \right)\to \left(\phi \to \forall x\psi \right)$$