Description: e110 without virtual deductions. (Contributed by Alan Sare, 22-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)
| Ref | Expression | ||
|---|---|---|---|
| Hypotheses | ee110.1 | |- ( ph -> ps ) |
|
| ee110.2 | |- ( ph -> ch ) |
||
| ee110.3 | |- th |
||
| ee110.4 | |- ( ps -> ( ch -> ( th -> ta ) ) ) |
||
| Assertion | ee110 | |- ( ph -> ta ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | ee110.1 | |- ( ph -> ps ) |
|
| 2 | ee110.2 | |- ( ph -> ch ) |
|
| 3 | ee110.3 | |- th |
|
| 4 | ee110.4 | |- ( ps -> ( ch -> ( th -> ta ) ) ) |
|
| 5 | 3 | a1i | |- ( ph -> th ) |
| 6 | 1 2 5 4 | syl3c | |- ( ph -> ta ) |