Metamath Proof Explorer


Theorem frege59b

Description: A kind of Aristotelian inference. Namely Felapton or Fesapo. Proposition 59 of Frege1879 p. 51.

Note: in the Bauer-Meenfelberg translation published in van Heijenoort's collectionFrom Frege to Goedel, this proof has the frege12 incorrectly referenced where frege30 is in the original. (Contributed by RP, 24-Dec-2019) (Proof modification is discouraged.)

Ref Expression
Assertion frege59b yxφ¬yxψ¬xφψ

Proof

Step Hyp Ref Expression
1 frege58bcor xφψyxφyxψ
2 frege30 xφψyxφyxψyxφ¬yxψ¬xφψ
3 1 2 ax-mp yxφ¬yxψ¬xφψ