Description: e202 without virtual deductions. (Contributed by Alan Sare, 13-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)
| Ref | Expression | ||
|---|---|---|---|
| Hypotheses | ee202.1 | |- ( ph -> ( ps -> ch ) ) |
|
| ee202.2 | |- th |
||
| ee202.3 | |- ( ph -> ( ps -> ta ) ) |
||
| ee202.4 | |- ( ch -> ( th -> ( ta -> et ) ) ) |
||
| Assertion | ee202 | |- ( ph -> ( ps -> et ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | ee202.1 | |- ( ph -> ( ps -> ch ) ) |
|
| 2 | ee202.2 | |- th |
|
| 3 | ee202.3 | |- ( ph -> ( ps -> ta ) ) |
|
| 4 | ee202.4 | |- ( ch -> ( th -> ( ta -> et ) ) ) |
|
| 5 | 2 | a1i | |- ( ps -> th ) |
| 6 | 5 | a1i | |- ( ph -> ( ps -> th ) ) |
| 7 | 1 6 3 4 | ee222 | |- ( ph -> ( ps -> et ) ) |