Description: Consequence of the definition of not-free. (Contributed by Mario Carneiro, 26-Sep-2016) df-nf changed. (Revised by Wolf Lammen, 11-Sep-2021) (Proof shortened by Wolf Lammen, 23-Nov-2023)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | nf5r | |- ( F/ x ph -> ( ph -> A. x ph ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | 19.8a | |- ( ph -> E. x ph ) |
|
| 2 | id | |- ( F/ x ph -> F/ x ph ) |
|
| 3 | 2 | nfrd | |- ( F/ x ph -> ( E. x ph -> A. x ph ) ) |
| 4 | 1 3 | syl5 | |- ( F/ x ph -> ( ph -> A. x ph ) ) |