Description: Conjunction form of e10 . (Contributed by Alan Sare, 15-Jun-2011) (Proof modification is discouraged.) (New usage is discouraged.)
Ref | Expression | ||
---|---|---|---|
Hypotheses | e10an.1 | |- (. ph ->. ps ). |
|
e10an.2 | |- ch |
||
e10an.3 | |- ( ( ps /\ ch ) -> th ) |
||
Assertion | e10an | |- (. ph ->. th ). |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | e10an.1 | |- (. ph ->. ps ). |
|
2 | e10an.2 | |- ch |
|
3 | e10an.3 | |- ( ( ps /\ ch ) -> th ) |
|
4 | 3 | ex | |- ( ps -> ( ch -> th ) ) |
5 | 1 2 4 | e10 | |- (. ph ->. th ). |