Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 24-Jun-2011) (Proof modification is discouraged.) (New usage is discouraged.)
Ref | Expression | ||
---|---|---|---|
Hypotheses | e30an.1 | |- (. ph ,. ps ,. ch ->. th ). |
|
e30an.2 | |- ta |
||
e30an.3 | |- ( ( th /\ ta ) -> et ) |
||
Assertion | e30an | |- (. ph ,. ps ,. ch ->. et ). |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | e30an.1 | |- (. ph ,. ps ,. ch ->. th ). |
|
2 | e30an.2 | |- ta |
|
3 | e30an.3 | |- ( ( th /\ ta ) -> et ) |
|
4 | 3 | ex | |- ( th -> ( ta -> et ) ) |
5 | 1 2 4 | e30 | |- (. ph ,. ps ,. ch ->. et ). |