Description: Weak version of hbe1 . See comments for ax10w . Uses only Tarski's FOL axiom schemes. (Contributed by NM, 19-Apr-2017)
| Ref | Expression | ||
|---|---|---|---|
| Hypothesis | hbn1w.1 | |- ( x = y -> ( ph <-> ps ) ) |
|
| Assertion | hbe1w | |- ( E. x ph -> A. x E. x ph ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | hbn1w.1 | |- ( x = y -> ( ph <-> ps ) ) |
|
| 2 | df-ex | |- ( E. x ph <-> -. A. x -. ph ) |
|
| 3 | 1 | notbid | |- ( x = y -> ( -. ph <-> -. ps ) ) |
| 4 | 3 | hbn1w | |- ( -. A. x -. ph -> A. x -. A. x -. ph ) |
| 5 | 2 4 | hbxfrbi | |- ( E. x ph -> A. x E. x ph ) |