Description: Conversion of double implicit substitution to explicit substitution. Version of 2sbiev with more disjoint variable conditions, requiring fewer axioms. (Contributed by AV, 29-Jul-2023) Avoid ax-13 . (Revised by GG, 10-Jan-2024)
| Ref | Expression | ||
|---|---|---|---|
| Hypothesis | 2sbievw.1 | |- ( ( x = t /\ y = u ) -> ( ph <-> ps ) ) |
|
| Assertion | 2sbievw | |- ( [ t / x ] [ u / y ] ph <-> ps ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | 2sbievw.1 | |- ( ( x = t /\ y = u ) -> ( ph <-> ps ) ) |
|
| 2 | 1 | sbiedvw | |- ( x = t -> ( [ u / y ] ph <-> ps ) ) |
| 3 | 2 | sbievw | |- ( [ t / x ] [ u / y ] ph <-> ps ) |