Theorem hbng

Description: A more general form of hbn . (Contributed by Scott Fenton, 13-Dec-2010)

	Ref	Expression
Hypothesis	hbg.1	$$⊢\phi \to \forall x\psi$$
Assertion	hbng	$$⊢\neg \psi \to \forall x\neg \phi$$

Proof

Step	Hyp	Ref	Expression
1		hbg.1	$$⊢\phi \to \forall x\psi$$
2		hbntg	$$⊢\forall x\left(\phi \to \forall x\psi \right)\to \left(\neg \psi \to \forall x\neg \phi \right)$$
3	2 1	mpg	$$⊢\neg \psi \to \forall x\neg \phi$$