Description: e020 without virtual deductions. (Contributed by Alan Sare, 13-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)
Ref | Expression | ||
---|---|---|---|
Hypotheses | ee020.1 | |- ph |
|
ee020.2 | |- ( ps -> ( ch -> th ) ) |
||
ee020.3 | |- ta |
||
ee020.4 | |- ( ph -> ( th -> ( ta -> et ) ) ) |
||
Assertion | ee020 | |- ( ps -> ( ch -> et ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ee020.1 | |- ph |
|
2 | ee020.2 | |- ( ps -> ( ch -> th ) ) |
|
3 | ee020.3 | |- ta |
|
4 | ee020.4 | |- ( ph -> ( th -> ( ta -> et ) ) ) |
|
5 | 1 | a1i | |- ( ch -> ph ) |
6 | 5 | a1i | |- ( ps -> ( ch -> ph ) ) |
7 | 3 | a1i | |- ( ch -> ta ) |
8 | 7 | a1i | |- ( ps -> ( ch -> ta ) ) |
9 | 6 2 8 4 | ee222 | |- ( ps -> ( ch -> et ) ) |