Theorem frege59b 38198

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 collection From Frege to Goedel, this proof has the frege12 38107 incorrectly referenced where frege30 38126 is in the original. (Contributed by RP, 24-Dec-2019.) (Proof modification is discouraged.)

Assertion

Ref	Expression
frege59b	|- ( [ x / y ] ph -> ( -. [ x / y ] ps -> -. A. y ( ph -> ps ) ) )

Proof of Theorem frege59b

Step	Hyp	Ref	Expression
1		frege58bcor 38197	. 2 |- ( A. y ( ph -> ps ) -> ( [ x / y ] ph -> [ x / y ] ps ) )
2		frege30 38126	. 2 |- ( ( A. y ( ph -> ps ) -> ( [ x / y ] ph -> [ x / y ] ps ) ) -> ( [ x / y ] ph -> ( -. [ x / y ] ps -> -. A. y ( ph -> ps ) ) ) )
3	1, 2	ax-mp 5	1 |- ( [ x / y ] ph -> ( -. [ x / y ] ps -> -. A. y ( ph -> ps ) ) )

Syntax hints:   -. wn 3   -> wi 4   A.wal 1481   [wsb 1880

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-10 2019  ax-12 2047  ax-13 2246  ax-frege1 38084  ax-frege2 38085  ax-frege8 38103  ax-frege28 38124  ax-frege58b 38195

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-ex 1705  df-nf 1710  df-sb 1881

This theorem is referenced by: (None)