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 ). |
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 ). |