Description: A virtual deduction elimination rule (see sylsyld ). (Contributed by Alan Sare, 21-Apr-2011) (Proof modification is discouraged.) (New usage is discouraged.)
Ref | Expression | ||
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Hypotheses | e12.1 | |- (. ph ->. ps ). |
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e12.2 | |- (. ph ,. ch ->. th ). |
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e12.3 | |- ( ps -> ( th -> ta ) ) |
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Assertion | e12 | |- (. ph ,. ch ->. ta ). |
Step | Hyp | Ref | Expression |
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1 | e12.1 | |- (. ph ->. ps ). |
|
2 | e12.2 | |- (. ph ,. ch ->. th ). |
|
3 | e12.3 | |- ( ps -> ( th -> ta ) ) |
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4 | 1 | vd12 | |- (. ph ,. ch ->. ps ). |
5 | 4 2 3 | e22 | |- (. ph ,. ch ->. ta ). |