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 | e221.1 | |- (. ph ,. ps ->. ch ). |
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e221.2 | |- (. ph ,. ps ->. th ). |
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e221.3 | |- (. ph ->. ta ). |
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e221.4 | |- ( ch -> ( th -> ( ta -> et ) ) ) |
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Assertion | e221 | |- (. ph ,. ps ->. et ). |
Step | Hyp | Ref | Expression |
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1 | e221.1 | |- (. ph ,. ps ->. ch ). |
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2 | e221.2 | |- (. ph ,. ps ->. th ). |
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3 | e221.3 | |- (. ph ->. ta ). |
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4 | e221.4 | |- ( ch -> ( th -> ( ta -> et ) ) ) |
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5 | 3 | vd12 | |- (. ph ,. ps ->. ta ). |
6 | 1 2 5 4 | e222 | |- (. ph ,. ps ->. et ). |