Description: Conjunction form of e03 . (Contributed by Alan Sare, 12-Jun-2011) (Proof modification is discouraged.) (New usage is discouraged.)
Ref | Expression | ||
---|---|---|---|
Hypotheses | e03an.1 | |- ph |
|
e03an.2 | |- (. ps ,. ch ,. th ->. ta ). |
||
e03an.3 | |- ( ( ph /\ ta ) -> et ) |
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Assertion | e03an | |- (. ps ,. ch ,. th ->. et ). |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | e03an.1 | |- ph |
|
2 | e03an.2 | |- (. ps ,. ch ,. th ->. ta ). |
|
3 | e03an.3 | |- ( ( ph /\ ta ) -> et ) |
|
4 | 3 | ex | |- ( ph -> ( ta -> et ) ) |
5 | 1 2 4 | e03 | |- (. ps ,. ch ,. th ->. et ). |