Description: equid with existential quantifier without using ax-c5 or ax-5 . (Contributed by NM, 13-Jan-2011) (Proof shortened by Wolf Lammen, 27-Feb-2014) (Proof modification is discouraged.) (New usage is discouraged.)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | equidqe | |- -. A. y -. x = x |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | ax6fromc10 | |- -. A. y -. y = x |
|
| 2 | ax7 | |- ( y = x -> ( y = x -> x = x ) ) |
|
| 3 | 2 | pm2.43i | |- ( y = x -> x = x ) |
| 4 | 3 | con3i | |- ( -. x = x -> -. y = x ) |
| 5 | 4 | alimi | |- ( A. y -. x = x -> A. y -. y = x ) |
| 6 | 1 5 | mto | |- -. A. y -. x = x |