Description: Conjunction form of e33 . (Contributed by Alan Sare, 15-Jun-2011) (Proof modification is discouraged.) (New usage is discouraged.)
Ref | Expression | ||
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Hypotheses | e33an.1 | |- (. ph ,. ps ,. ch ->. th ). |
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e33an.2 | |- (. ph ,. ps ,. ch ->. ta ). |
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e33an.3 | |- ( ( th /\ ta ) -> et ) |
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Assertion | e33an | |- (. ph ,. ps ,. ch ->. et ). |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | e33an.1 | |- (. ph ,. ps ,. ch ->. th ). |
|
2 | e33an.2 | |- (. ph ,. ps ,. ch ->. ta ). |
|
3 | e33an.3 | |- ( ( th /\ ta ) -> et ) |
|
4 | 3 | ex | |- ( th -> ( ta -> et ) ) |
5 | 1 2 4 | e33 | |- (. ph ,. ps ,. ch ->. et ). |