Description: A biconditional form of equvel with disjoint variable conditions and proved from Tarski's FOL axiom schemes. (Contributed by Andrew Salmon, 2-Jun-2011) Reduce axiom usage. (Revised by Wolf Lammen, 10-Apr-2021) (Proof shortened by Wolf Lammen, 12-Jul-2022)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | equvelv | |- ( A. z ( z = x -> z = y ) <-> x = y ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | equequ1 | |- ( z = x -> ( z = y <-> x = y ) ) |
|
| 2 | 1 | equsalvw | |- ( A. z ( z = x -> z = y ) <-> x = y ) |