Description: e112 without virtual deductions. (Contributed by Alan Sare, 13-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)
| Ref | Expression | ||
|---|---|---|---|
| Hypotheses | ee112.1 | |- ( ph -> ps ) |
|
| ee112.2 | |- ( ph -> ch ) |
||
| ee112.3 | |- ( ph -> ( th -> ta ) ) |
||
| ee112.4 | |- ( ps -> ( ch -> ( ta -> et ) ) ) |
||
| Assertion | ee112 | |- ( ph -> ( th -> et ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | ee112.1 | |- ( ph -> ps ) |
|
| 2 | ee112.2 | |- ( ph -> ch ) |
|
| 3 | ee112.3 | |- ( ph -> ( th -> ta ) ) |
|
| 4 | ee112.4 | |- ( ps -> ( ch -> ( ta -> et ) ) ) |
|
| 5 | 1 | a1d | |- ( ph -> ( th -> ps ) ) |
| 6 | 2 | a1d | |- ( ph -> ( th -> ch ) ) |
| 7 | 5 6 3 4 | ee222 | |- ( ph -> ( th -> et ) ) |