Description: Virtual deduction generalizing rule for two quantifying variables and one virtual hypothesis. gen12 is alrimivv with virtual deductions. (Contributed by Alan Sare, 2-May-2011) (Proof modification is discouraged.) (New usage is discouraged.)
Ref | Expression | ||
---|---|---|---|
Hypothesis | gen12.1 | |- (. ph ->. ps ). |
|
Assertion | gen12 | |- (. ph ->. A. x A. y ps ). |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | gen12.1 | |- (. ph ->. ps ). |
|
2 | 1 | in1 | |- ( ph -> ps ) |
3 | 2 | alrimivv | |- ( ph -> A. x A. y ps ) |
4 | 3 | dfvd1ir | |- (. ph ->. A. x A. y ps ). |