Description: An equivalence law for equality. (Contributed by NM, 21-Jun-1993) (Proof shortened by Wolf Lammen, 4-Aug-2017) (Proof shortened by BJ, 12-Apr-2021)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | equequ2 | |- ( x = y -> ( z = x <-> z = y ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | equtrr | |- ( x = y -> ( z = x -> z = y ) ) |
|
| 2 | equeuclr | |- ( x = y -> ( z = y -> z = x ) ) |
|
| 3 | 1 2 | impbid | |- ( x = y -> ( z = x <-> z = y ) ) |