Theorem gen12

Description: Virtual deduction generalizing rule for two quantifying variables and one virtual hypothesis. gen12 is alrimivv with virtual deductions. (Contributed by Alan Sare, 2-May-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypothesis	gen12.1	$$⊢\left(\phi \to \psi \right)$$
Assertion	gen12	$$⊢\left(\phi \to \forall x\forall y\psi \right)$$

Proof

Step	Hyp	Ref	Expression
1		gen12.1	$$⊢\left(\phi \to \psi \right)$$
2	1	in1	$$⊢\phi \to \psi$$
3	2	alrimivv	$$⊢\phi \to \forall x\forall y\psi$$
4	3	dfvd1ir	$$⊢\left(\phi \to \forall x\forall y\psi \right)$$