Description: Closed theorem version of bound-variable hypothesis builder hbn . (Contributed by NM, 10-May-1993) (Proof shortened by Wolf Lammen, 14-Oct-2021)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | hbnt | |- ( A. x ( ph -> A. x ph ) -> ( -. ph -> A. x -. ph ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | nf5-1 | |- ( A. x ( ph -> A. x ph ) -> F/ x ph ) |
|
| 2 | 1 | nfnd | |- ( A. x ( ph -> A. x ph ) -> F/ x -. ph ) |
| 3 | 2 | nf5rd | |- ( A. x ( ph -> A. x ph ) -> ( -. ph -> A. x -. ph ) ) |