Description: If x is not free in ph , it is not free in -. ph . (Contributed by NM, 10-Jan-1993) (Proof shortened by Wolf Lammen, 17-Dec-2017)
| Ref | Expression | ||
|---|---|---|---|
| Hypothesis | hbn.1 | |- ( ph -> A. x ph ) |
|
| Assertion | hbn | |- ( -. ph -> A. x -. ph ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | hbn.1 | |- ( ph -> A. x ph ) |
|
| 2 | hbnt | |- ( A. x ( ph -> A. x ph ) -> ( -. ph -> A. x -. ph ) ) |
|
| 3 | 2 1 | mpg | |- ( -. ph -> A. x -. ph ) |