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 ) ) |