Description: Virtual deduction generalizing rule for one quantifying variable and one virtual hypothesis. alrimiv is gen11 without virtual deductions. (Contributed by Alan Sare, 21-Apr-2011) (Proof modification is discouraged.) (New usage is discouraged.)
Ref | Expression | ||
---|---|---|---|
Hypothesis | gen11.1 | |- (. ph ->. ps ). |
|
Assertion | gen11 | |- (. ph ->. A. x ps ). |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | gen11.1 | |- (. ph ->. ps ). |
|
2 | dfvd1imp | |- ( (. ph ->. ps ). -> ( ph -> ps ) ) |
|
3 | 1 2 | ax-mp | |- ( ph -> ps ) |
4 | 3 | alrimiv | |- ( ph -> A. x ps ) |
5 | dfvd1impr | |- ( ( ph -> A. x ps ) -> (. ph ->. A. x ps ). ) |
|
6 | 4 5 | ax-mp | |- (. ph ->. A. x ps ). |