Description: Distinct-variable version of spime . Usage of this theorem is discouraged because it depends on ax-13 . Use the weaker spimevw if possible. (Contributed by NM, 10-Jan-1993) (New usage is discouraged.)
| Ref | Expression | ||
|---|---|---|---|
| Hypothesis | spimev.1 | |- ( x = y -> ( ph -> ps ) ) |
|
| Assertion | spimev | |- ( ph -> E. x ps ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | spimev.1 | |- ( x = y -> ( ph -> ps ) ) |
|
| 2 | nfv | |- F/ x ph |
|
| 3 | 2 1 | spime | |- ( ph -> E. x ps ) |