Description: Under the assumption -. x = y a specialized version of sp is provable from Tarski's FOL and ax13v only. Note that this reverts the implication in ax13lem1 , so in fact ( -. x = y -> ( A. x z = y <-> z = y ) ) holds. (Contributed by Wolf Lammen, 17-Apr-2021)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | wl-speqv | |- ( -. x = y -> ( A. x z = y -> z = y ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | 19.2 | |- ( A. x z = y -> E. x z = y ) |
|
| 2 | ax13lem2 | |- ( -. x = y -> ( E. x z = y -> z = y ) ) |
|
| 3 | 1 2 | syl5 | |- ( -. x = y -> ( A. x z = y -> z = y ) ) |