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 | e202.1 | |- (. ph ,. ps ->. ch ). |
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e202.2 | |- th |
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e202.3 | |- (. ph ,. ps ->. ta ). |
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e202.4 | |- ( ch -> ( th -> ( ta -> et ) ) ) |
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Assertion | e202 | |- (. ph ,. ps ->. et ). |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | e202.1 | |- (. ph ,. ps ->. ch ). |
|
2 | e202.2 | |- th |
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3 | e202.3 | |- (. ph ,. ps ->. ta ). |
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4 | e202.4 | |- ( ch -> ( th -> ( ta -> et ) ) ) |
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5 | 2 | vd02 | |- (. ph ,. ps ->. th ). |
6 | 1 5 3 4 | e222 | |- (. ph ,. ps ->. et ). |