Given our substitution rules, all the rules of the classical Aristotelian syllogism can be condensed to two basic patterns:
FGD, GHD |- FHD -- DD inf (short for DD inference)
FGE, GHD |- FHE -- ED inf
These shortcut rules allow us to work through many derivations very easily, as in the following examples.
FGAHD, HJKOD, FGE, JNV |- KW
1. FGAHD
2. HJKOD
3. FGE
4. JNV \ show KW
5. FGAJKOD..........1,2 DD inf
6. FaGaA...............3 Elim
7. FaGaAJaKaOC... 5 Delim
8. JaKaO...............6,7 C elim
9. JNa...................4 V elim
10. Ka...................8,9 O elim
11. KW..................10 W int
FGNE, HGD, HNJD |- FJE
1. FGNE
2. HGD
3. HNJD \ show FJE
4. GNHND........2 D subs
5. FHNE...........1,4 ED inf
6. FJE..............3,5 ED inf
Go ahead to indirect derivations.
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