Description: Specialization, with additional weakening (compared to 19.2 ) to allow bundling of x and y . Uses only Tarski's FOL axiom schemes. (Contributed by NM, 23-Apr-2017) (Proof shortened by Wolf Lammen, 5-Dec-2017)
| Ref | Expression | ||
|---|---|---|---|
| Hypothesis | speimfw.2 | |- ( x = y -> ( ph -> ps ) ) |
|
| Assertion | speimfw | |- ( -. A. x -. x = y -> ( A. x ph -> E. x ps ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | speimfw.2 | |- ( x = y -> ( ph -> ps ) ) |
|
| 2 | df-ex | |- ( E. x x = y <-> -. A. x -. x = y ) |
|
| 3 | 2 | biimpri | |- ( -. A. x -. x = y -> E. x x = y ) |
| 4 | 1 | com12 | |- ( ph -> ( x = y -> ps ) ) |
| 5 | 4 | aleximi | |- ( A. x ph -> ( E. x x = y -> E. x ps ) ) |
| 6 | 3 5 | syl5com | |- ( -. A. x -. x = y -> ( A. x ph -> E. x ps ) ) |