Description: Change bound variable in an equality with a disjoint variable condition. Instance of aev . (Contributed by NM, 22-Jul-2015) (Revised by BJ, 18-Jun-2019)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | cbvaev | |- ( A. x x = y -> A. z z = y ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | ax7 | |- ( x = t -> ( x = y -> t = y ) ) |
|
| 2 | 1 | cbvalivw | |- ( A. x x = y -> A. t t = y ) |
| 3 | ax7 | |- ( t = z -> ( t = y -> z = y ) ) |
|
| 4 | 3 | cbvalivw | |- ( A. t t = y -> A. z z = y ) |
| 5 | 2 4 | syl | |- ( A. x x = y -> A. z z = y ) |