Description: Deduction version of spimev . Version of spimed with a disjoint variable condition, which does not require ax-13 . See spime for a non-deduction version. (Contributed by NM, 14-May-1993) (Revised by BJ, 31-May-2019)
| Ref | Expression | ||
|---|---|---|---|
| Hypotheses | spimedv.1 | |- ( ch -> F/ x ph ) |
|
| spimedv.2 | |- ( x = y -> ( ph -> ps ) ) |
||
| Assertion | spimedv | |- ( ch -> ( ph -> E. x ps ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | spimedv.1 | |- ( ch -> F/ x ph ) |
|
| 2 | spimedv.2 | |- ( x = y -> ( ph -> ps ) ) |
|
| 3 | 1 | nf5rd | |- ( ch -> ( ph -> A. x ph ) ) |
| 4 | ax6ev | |- E. x x = y |
|
| 5 | 4 2 | eximii | |- E. x ( ph -> ps ) |
| 6 | 5 | 19.35i | |- ( A. x ph -> E. x ps ) |
| 7 | 3 6 | syl6 | |- ( ch -> ( ph -> E. x ps ) ) |