Description: Deduction combining antecedents and consequents. Deduction associated with imim12 and imim12i . (Contributed by NM, 7-Aug-1994) (Proof shortened by Mel L. O'Cat, 30-Oct-2011)
| Ref | Expression | ||
|---|---|---|---|
| Hypotheses | imim12d.1 | |- ( ph -> ( ps -> ch ) ) |
|
| imim12d.2 | |- ( ph -> ( th -> ta ) ) |
||
| Assertion | imim12d | |- ( ph -> ( ( ch -> th ) -> ( ps -> ta ) ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | imim12d.1 | |- ( ph -> ( ps -> ch ) ) |
|
| 2 | imim12d.2 | |- ( ph -> ( th -> ta ) ) |
|
| 3 | 2 | imim2d | |- ( ph -> ( ( ch -> th ) -> ( ch -> ta ) ) ) |
| 4 | 1 3 | syl5d | |- ( ph -> ( ( ch -> th ) -> ( ps -> ta ) ) ) |