Description: Quantifier introduction when one pair of variables is distinct. Usage of this theorem is discouraged because it depends on ax-13 . (Contributed by NM, 2-Jan-2002) Remove dependency on ax-11 . (Revised by Wolf Lammen, 8-Sep-2018) (New usage is discouraged.)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | dveeq1 | |- ( -. A. x x = y -> ( y = z -> A. x y = z ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | nfeqf1 | |- ( -. A. x x = y -> F/ x y = z ) |
|
| 2 | 1 | nf5rd | |- ( -. A. x x = y -> ( y = z -> A. x y = z ) ) |