Theorem gen21nv 38845

Description: Virtual deduction form of alrimdh 1790. (Contributed by Alan Sare, 31-Dec-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
gen21nv.1	|- ( ph -> A. x ph )
gen21nv.2	|- ( ps -> A. x ps )
gen21nv.3	|- (. ph ,. ps ->. ch ).

Assertion

Ref	Expression
gen21nv	|- (. ph ,. ps ->. A. x ch ).

Proof of Theorem gen21nv

Step	Hyp	Ref	Expression
1		gen21nv.1	. . 3 |- ( ph -> A. x ph )
2		gen21nv.2	. . 3 |- ( ps -> A. x ps )
3		gen21nv.3	. . . 4 |- (. ph ,. ps ->. ch ).
4	3	dfvd2i 38801	. . 3 |- ( ph -> ( ps -> ch ) )
5	1, 2, 4	alrimdh 1790	. 2 |- ( ph -> ( ps -> A. x ch ) )
6	5	dfvd2ir 38802	1 |- (. ph ,. ps ->. A. x ch ).

Syntax hints:   -> wi 4   A.wal 1481   (.wvd2 38793

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737

This theorem depends on definitions:  df-bi 197  df-an 386  df-vd2 38794

This theorem is referenced by:  ssralv2VD  39102