Description: e010 without virtual deductions. (Contributed by Alan Sare, 23-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)
| Ref | Expression | ||
|---|---|---|---|
| Hypotheses | ee010.1 | |- ph |
|
| ee010.2 | |- ( ps -> ch ) |
||
| ee010.3 | |- th |
||
| ee010.4 | |- ( ph -> ( ch -> ( th -> ta ) ) ) |
||
| Assertion | ee010 | |- ( ps -> ta ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | ee010.1 | |- ph |
|
| 2 | ee010.2 | |- ( ps -> ch ) |
|
| 3 | ee010.3 | |- th |
|
| 4 | ee010.4 | |- ( ph -> ( ch -> ( th -> ta ) ) ) |
|
| 5 | 1 | a1i | |- ( ps -> ph ) |
| 6 | 3 | a1i | |- ( ps -> th ) |
| 7 | 5 2 6 4 | syl3c | |- ( ps -> ta ) |