Description: Weak version of excomim . Uses only Tarski's FOL axiom schemes. (Contributed by BTernaryTau, 23-Jun-2025)
Ref | Expression | ||
---|---|---|---|
Hypothesis | excomimw.1 | |- ( x = z -> ( ph <-> ps ) ) |
|
Assertion | excomimw | |- ( E. x E. y ph -> E. y E. x ph ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | excomimw.1 | |- ( x = z -> ( ph <-> ps ) ) |
|
2 | 1 | notbid | |- ( x = z -> ( -. ph <-> -. ps ) ) |
3 | 2 | alcomimw | |- ( A. y A. x -. ph -> A. x A. y -. ph ) |
4 | 3 | con3i | |- ( -. A. x A. y -. ph -> -. A. y A. x -. ph ) |
5 | 2exnaln | |- ( E. x E. y ph <-> -. A. x A. y -. ph ) |
|
6 | 2exnaln | |- ( E. y E. x ph <-> -. A. y A. x -. ph ) |
|
7 | 4 5 6 | 3imtr4i | |- ( E. x E. y ph -> E. y E. x ph ) |