Description: e100 without virtual deductions. (Contributed by Alan Sare, 23-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)
| Ref | Expression | ||
|---|---|---|---|
| Hypotheses | ee100.1 | |- ( ph -> ps ) |
|
| ee100.2 | |- ch |
||
| ee100.3 | |- th |
||
| ee100.4 | |- ( ps -> ( ch -> ( th -> ta ) ) ) |
||
| Assertion | ee100 | |- ( ph -> ta ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | ee100.1 | |- ( ph -> ps ) |
|
| 2 | ee100.2 | |- ch |
|
| 3 | ee100.3 | |- th |
|
| 4 | ee100.4 | |- ( ps -> ( ch -> ( th -> ta ) ) ) |
|
| 5 | 2 | a1i | |- ( ph -> ch ) |
| 6 | 3 | a1i | |- ( ph -> th ) |
| 7 | 1 5 6 4 | syl3c | |- ( ph -> ta ) |