Description: Version of sb4a with a disjoint variable condition, which does not require ax-13 . The distinctor antecedent from sb4b is replaced by a disjoint variable condition in this theorem. (Contributed by NM, 2-Feb-2007) (Revised by BJ, 15-Dec-2023)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | sb4av | |- ( [ t / x ] A. t ph -> A. x ( x = t -> ph ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | sp | |- ( A. t ph -> ph ) |
|
| 2 | 1 | sbimi | |- ( [ t / x ] A. t ph -> [ t / x ] ph ) |
| 3 | sb6 | |- ( [ t / x ] ph <-> A. x ( x = t -> ph ) ) |
|
| 4 | 2 3 | sylib | |- ( [ t / x ] A. t ph -> A. x ( x = t -> ph ) ) |