Metamath Proof Explorer


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 ).