Description: Syllogism inference combined with modus ponens. (Contributed by Jeff Madsen, 2-Sep-2009) (Revised by Alan Sare, 23-Dec-2016) (Proof modification is discouraged.) (New usage is discouraged.)
| Ref | Expression | ||
|---|---|---|---|
| Hypotheses | eelT1.1 | |- ( T. -> ph ) |
|
| eelT1.2 | |- ( ps -> ch ) |
||
| eelT1.3 | |- ( ( ph /\ ch ) -> th ) |
||
| Assertion | eelT1 | |- ( ps -> th ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | eelT1.1 | |- ( T. -> ph ) |
|
| 2 | eelT1.2 | |- ( ps -> ch ) |
|
| 3 | eelT1.3 | |- ( ( ph /\ ch ) -> th ) |
|
| 4 | 1 | mptru | |- ph |
| 5 | 4 2 3 | sylancr | |- ( ps -> th ) |