Description: Alternate proof of speimfw (longer compressed proof, but fewer essential steps). (Contributed by NM, 23-Apr-2017) (Proof shortened by Wolf Lammen, 5-Aug-2017) (Proof modification is discouraged.) (New usage is discouraged.)
| Ref | Expression | ||
|---|---|---|---|
| Hypothesis | speimfw.2 | |- ( x = y -> ( ph -> ps ) ) |
|
| Assertion | speimfwALT | |- ( -. A. x -. x = y -> ( A. x ph -> E. x ps ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | speimfw.2 | |- ( x = y -> ( ph -> ps ) ) |
|
| 2 | 1 | eximi | |- ( E. x x = y -> E. x ( ph -> ps ) ) |
| 3 | df-ex | |- ( E. x x = y <-> -. A. x -. x = y ) |
|
| 4 | 19.35 | |- ( E. x ( ph -> ps ) <-> ( A. x ph -> E. x ps ) ) |
|
| 5 | 2 3 4 | 3imtr3i | |- ( -. A. x -. x = y -> ( A. x ph -> E. x ps ) ) |