Theorem ggen22

Description: gen22 without virtual deductions. (Contributed by Alan Sare, 25-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypothesis	ggen22.1	$$⊢\phi \to \left(\psi \to \chi \right)$$
Assertion	ggen22	$$⊢\phi \to \left(\psi \to \forall x\forall y\chi \right)$$

Proof

Step	Hyp	Ref	Expression
1		ggen22.1	$$⊢\phi \to \left(\psi \to \chi \right)$$
2	1	alrimdv	$$⊢\phi \to \left(\psi \to \forall y\chi \right)$$
3	2	alrimdv	$$⊢\phi \to \left(\psi \to \forall x\forall y\chi \right)$$