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	|- ( [ y / x ] ph -> ( -. [ y / x ] ps -> -. A. x ( ph -> ps ) ) )

Proof

Step	Hyp	Ref	Expression
1		frege58bcor	|- ( A. x ( ph -> ps ) -> ( [ y / x ] ph -> [ y / x ] ps ) )
2		frege30	|- ( ( A. x ( ph -> ps ) -> ( [ y / x ] ph -> [ y / x ] ps ) ) -> ( [ y / x ] ph -> ( -. [ y / x ] ps -> -. A. x ( ph -> ps ) ) ) )
3	1 2	ax-mp	|- ( [ y / x ] ph -> ( -. [ y / x ] ps -> -. A. x ( ph -> ps ) ) )