Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 24-Jun-2011) (Proof modification is discouraged.) (New usage is discouraged.)
Ref | Expression | ||
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Hypotheses | e23an.1 | |- (. ph ,. ps ->. ch ). |
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e23an.2 | |- (. ph ,. ps ,. th ->. ta ). |
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e23an.3 | |- ( ( ch /\ ta ) -> et ) |
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Assertion | e23an | |- (. ph ,. ps ,. th ->. et ). |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | e23an.1 | |- (. ph ,. ps ->. ch ). |
|
2 | e23an.2 | |- (. ph ,. ps ,. th ->. ta ). |
|
3 | e23an.3 | |- ( ( ch /\ ta ) -> et ) |
|
4 | 3 | ex | |- ( ch -> ( ta -> et ) ) |
5 | 1 2 4 | e23 | |- (. ph ,. ps ,. th ->. et ). |