Description: Alternate proof of ab0 , shorter but using more axioms. (Contributed by BJ, 19-Mar-2021) (Proof modification is discouraged.) (New usage is discouraged.)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | ab0ALT | |- ( { x | ph } = (/) <-> A. x -. ph ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | nfab1 | |- F/_ x { x | ph } |
|
| 2 | 1 | eq0f | |- ( { x | ph } = (/) <-> A. x -. x e. { x | ph } ) |
| 3 | abid | |- ( x e. { x | ph } <-> ph ) |
|
| 4 | 3 | notbii | |- ( -. x e. { x | ph } <-> -. ph ) |
| 5 | 4 | albii | |- ( A. x -. x e. { x | ph } <-> A. x -. ph ) |
| 6 | 2 5 | bitri | |- ( { x | ph } = (/) <-> A. x -. ph ) |