Description: Version of sp when ph is false. Uses only Tarski's FOL axiom schemes. (Contributed by NM, 23-Apr-2017) (Proof shortened by Wolf Lammen, 25-Dec-2017)
| Ref | Expression | ||
|---|---|---|---|
| Hypothesis | spfalw.1 | |- -. ph |
|
| Assertion | spfalw | |- ( A. x ph -> ph ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | spfalw.1 | |- -. ph |
|
| 2 | 1 | hbth | |- ( -. ph -> A. x -. ph ) |
| 3 | 2 | spnfw | |- ( A. x ph -> ph ) |