Description: Alternate proof of dveeq2 , shorter but requiring ax-11 . (Contributed by NM, 2-Jan-2002) (Revised by NM, 20-Jul-2015) (New usage is discouraged.) (Proof modification is discouraged.)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | dveeq2ALT | |- ( -. A. x x = y -> ( z = y -> A. x z = y ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | equequ2 | |- ( w = y -> ( z = w <-> z = y ) ) |
|
| 2 | 1 | dvelimv | |- ( -. A. x x = y -> ( z = y -> A. x z = y ) ) |