Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 13-Jun-2011) (Proof modification is discouraged.) (New usage is discouraged.)
Ref | Expression | ||
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Hypotheses | e31.1 | |- (. ph ,. ps ,. ch ->. th ). |
|
e31.2 | |- (. ph ->. ta ). |
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e31.3 | |- ( th -> ( ta -> et ) ) |
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Assertion | e31 | |- (. ph ,. ps ,. ch ->. et ). |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | e31.1 | |- (. ph ,. ps ,. ch ->. th ). |
|
2 | e31.2 | |- (. ph ->. ta ). |
|
3 | e31.3 | |- ( th -> ( ta -> et ) ) |
|
4 | 2 | vd13 | |- (. ph ,. ps ,. ch ->. ta ). |
5 | 1 4 3 | e33 | |- (. ph ,. ps ,. ch ->. et ). |