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	|- (. ph ,. ps ->. ch ).
Assertion	gen22	|- (. ph ,. ps ->. A. x A. y ch ).

Proof

Step	Hyp	Ref	Expression
1		gen22.1	|- (. ph ,. ps ->. ch ).
2	1	dfvd2i	|- ( ph -> ( ps -> ch ) )
3	2	alrimdv	|- ( ph -> ( ps -> A. y ch ) )
4	3	alrimdv	|- ( ph -> ( ps -> A. x A. y ch ) )
5	4	dfvd2ir	|- (. ph ,. ps ->. A. x A. y ch ).