Theorem gen21 37040

Description: Virtual deduction generalizing rule for one quantifying variables and two virtual hypothesis. gen21 37040 is alrimdv 1785 with virtual deductions. (Contributed by Alan Sare, 25-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypothesis

Ref	Expression
gen21.1	|- (. ph ,. ps ->. ch ).

Assertion

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

Distinct variable groups:   ph, x   ps, x

Allowed substitution hint:   ch( x)

Proof of Theorem gen21

Step	Hyp	Ref	Expression
1		gen21.1	. . . 4 |- (. ph ,. ps ->. ch ).
2	1	dfvd2i 36997	. . 3 |- ( ph -> ( ps -> ch ) )
3	2	alrimdv 1785	. 2 |- ( ph -> ( ps -> A. x ch ) )
4	3	dfvd2ir 36998	1 |- (. ph ,. ps ->. A. x ch ).

Syntax hints:   A.wal 1452   (.wvd2 36989

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1679  ax-4 1692  ax-5 1768

This theorem depends on definitions:  df-bi 190  df-an 377  df-vd2 36990

This theorem is referenced by:  truniALTVD  37314  trintALTVD  37316  onfrALTlem2VD  37325