Description: e022 without virtual deductions. (Contributed by Alan Sare, 13-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)
| Ref | Expression | ||
|---|---|---|---|
| Hypotheses | ee022.1 | |- ph |
|
| ee022.2 | |- ( ps -> ( ch -> th ) ) |
||
| ee022.3 | |- ( ps -> ( ch -> ta ) ) |
||
| ee022.4 | |- ( ph -> ( th -> ( ta -> et ) ) ) |
||
| Assertion | ee022 | |- ( ps -> ( ch -> et ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | ee022.1 | |- ph |
|
| 2 | ee022.2 | |- ( ps -> ( ch -> th ) ) |
|
| 3 | ee022.3 | |- ( ps -> ( ch -> ta ) ) |
|
| 4 | ee022.4 | |- ( ph -> ( th -> ( ta -> et ) ) ) |
|
| 5 | 1 | a1i | |- ( ch -> ph ) |
| 6 | 5 | a1i | |- ( ps -> ( ch -> ph ) ) |
| 7 | 6 2 3 4 | ee222 | |- ( ps -> ( ch -> et ) ) |