Description: Conversion of implicit substitution to explicit substitution. Version of sbie and sbiev with more disjoint variable conditions, requiring fewer axioms. (Contributed by NM, 30-Jun-1994) (Revised by BJ, 18-Jul-2023)
| Ref | Expression | ||
|---|---|---|---|
| Hypothesis | sbievw.is | |- ( x = y -> ( ph <-> ps ) ) |
|
| Assertion | sbievw | |- ( [ y / x ] ph <-> ps ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | sbievw.is | |- ( x = y -> ( ph <-> ps ) ) |
|
| 2 | sb6 | |- ( [ y / x ] ph <-> A. x ( x = y -> ph ) ) |
|
| 3 | 1 | equsalvw | |- ( A. x ( x = y -> ph ) <-> ps ) |
| 4 | 2 3 | bitri | |- ( [ y / x ] ph <-> ps ) |