Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 24-Jun-2011) (Proof modification is discouraged.) (New usage is discouraged.)
Ref | Expression | ||
---|---|---|---|
Hypotheses | e010.1 | |- ph |
|
e010.2 | |- (. ps ->. ch ). |
||
e010.3 | |- th |
||
e010.4 | |- ( ph -> ( ch -> ( th -> ta ) ) ) |
||
Assertion | e010 | |- (. ps ->. ta ). |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | e010.1 | |- ph |
|
2 | e010.2 | |- (. ps ->. ch ). |
|
3 | e010.3 | |- th |
|
4 | e010.4 | |- ( ph -> ( ch -> ( th -> ta ) ) ) |
|
5 | 1 | vd01 | |- (. ps ->. ph ). |
6 | 3 | vd01 | |- (. ps ->. th ). |
7 | 5 2 6 4 | e111 | |- (. ps ->. ta ). |