Theorem gen21

Description: Virtual deduction generalizing rule for one quantifying variables and two virtual hypothesis. gen21 is alrimdv with virtual deductions. (Contributed by Alan Sare, 25-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypothesis	gen21.1	|- (. ph ,. ps ->. ch ).
Assertion	gen21	|- (. ph ,. ps ->. A. x ch ).

Proof

Step	Hyp	Ref	Expression
1		gen21.1	|- (. ph ,. ps ->. ch ).
2	1	dfvd2i	|- ( ph -> ( ps -> ch ) )
3	2	alrimdv	|- ( ph -> ( ps -> A. x ch ) )
4	3	dfvd2ir	|- (. ph ,. ps ->. A. x ch ).