Description: Version of sp when x does not occur in ph . Converse of ax-5 . Uses only Tarski's FOL axiom schemes. (Contributed by NM, 10-Apr-2017) (Proof shortened by Wolf Lammen, 4-Dec-2017) Shorten 19.3v . (Revised by Wolf Lammen, 20-Oct-2023)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | spvw | |- ( A. x ph -> ph ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | ax-5 | |- ( -. ph -> A. x -. ph ) |
|
| 2 | 1 | spnfw | |- ( A. x ph -> ph ) |