Theorem gen21nv

Description: Virtual deduction form of alrimdh . (Contributed by Alan Sare, 31-Dec-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	gen21nv.1	$$⊢\phi \to \forall x\phi$$
	gen21nv.2	$$⊢\psi \to \forall x\psi$$
	gen21nv.3	$$⊢\left(\phi ,\psi \to \chi \right)$$
Assertion	gen21nv	$$⊢\left(\phi ,\psi \to \forall x\chi \right)$$

Proof

Step	Hyp	Ref	Expression
1		gen21nv.1	$$⊢\phi \to \forall x\phi$$
2		gen21nv.2	$$⊢\psi \to \forall x\psi$$
3		gen21nv.3	$$⊢\left(\phi ,\psi \to \chi \right)$$
4	3	dfvd2i	$$⊢\phi \to \left(\psi \to \chi \right)$$
5	1 2 4	alrimdh	$$⊢\phi \to \left(\psi \to \forall x\chi \right)$$
6	5	dfvd2ir	$$⊢\left(\phi ,\psi \to \forall x\chi \right)$$