Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 24-Jun-2011) (Proof modification is discouraged.) (New usage is discouraged.)
Ref | Expression | ||
---|---|---|---|
Hypotheses | e100.1 | |- (. ph ->. ps ). |
|
e100.2 | |- ch |
||
e100.3 | |- th |
||
e100.4 | |- ( ps -> ( ch -> ( th -> ta ) ) ) |
||
Assertion | e100 | |- (. ph ->. ta ). |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | e100.1 | |- (. ph ->. ps ). |
|
2 | e100.2 | |- ch |
|
3 | e100.3 | |- th |
|
4 | e100.4 | |- ( ps -> ( ch -> ( th -> ta ) ) ) |
|
5 | 2 | vd01 | |- (. ph ->. ch ). |
6 | 3 | vd01 | |- (. ph ->. th ). |
7 | 1 5 6 4 | e111 | |- (. ph ->. ta ). |