Description: Specialization, using implicit substitution. Usage of this theorem is discouraged because it depends on ax-13 . Use the weaker spvv if possible. (Contributed by NM, 30-Aug-1993) (New usage is discouraged.)
| Ref | Expression | ||
|---|---|---|---|
| Hypothesis | spv.1 | |- ( x = y -> ( ph <-> ps ) ) |
|
| Assertion | spv | |- ( A. x ph -> ps ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | spv.1 | |- ( x = y -> ( ph <-> ps ) ) |
|
| 2 | 1 | biimpd | |- ( x = y -> ( ph -> ps ) ) |
| 3 | 2 | spimv | |- ( A. x ph -> ps ) |