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	|- (. ph ->. ps ).
Assertion	gen12	|- (. ph ->. A. x A. y ps ).

Proof

Step	Hyp	Ref	Expression
1		gen12.1	|- (. ph ->. ps ).
2	1	in1	|- ( ph -> ps )
3	2	alrimivv	|- ( ph -> A. x A. y ps )
4	3	dfvd1ir	|- (. ph ->. A. x A. y ps ).