Theorem gen22

Description: Virtual deduction generalizing rule for two quantifying variables and two virtual hypothesis. (Contributed by Alan Sare, 25-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypothesis	gen22.1	$$⊢\left(\phi ,\psi \to \chi \right)$$
Assertion	gen22	$$⊢\left(\phi ,\psi \to \forall x\forall y\chi \right)$$

Proof

Step	Hyp	Ref	Expression
1		gen22.1	$$⊢\left(\phi ,\psi \to \chi \right)$$
2	1	dfvd2i	$$⊢\phi \to \left(\psi \to \chi \right)$$
3	2	alrimdv	$$⊢\phi \to \left(\psi \to \forall y\chi \right)$$
4	3	alrimdv	$$⊢\phi \to \left(\psi \to \forall x\forall y\chi \right)$$
5	4	dfvd2ir	$$⊢\left(\phi ,\psi \to \forall x\forall y\chi \right)$$