Description: Version of dveeq1 using ax-c16 instead of ax-5 . (Contributed by NM, 29-Apr-2008) TODO: Recover proof from older set.mm to remove use of ax-5 . (Proof modification is discouraged.) (New usage is discouraged.)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | dveeq1-o16 | |- ( -. A. x x = y -> ( y = z -> A. x y = z ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | ax5eq | |- ( w = z -> A. x w = z ) |
|
| 2 | ax5eq | |- ( y = z -> A. w y = z ) |
|
| 3 | equequ1 | |- ( w = y -> ( w = z <-> y = z ) ) |
|
| 4 | 1 2 3 | dvelimh | |- ( -. A. x x = y -> ( y = z -> A. x y = z ) ) |