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Theorem frege59b 38698
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 38607 incorrectly referenced where frege30 38626 is in the original. (Contributed by RP, 24-Dec-2019.) (Proof modification is discouraged.)

Assertion
Ref Expression
frege59b ([𝑥 / 𝑦]𝜑 → (¬ [𝑥 / 𝑦]𝜓 → ¬ ∀𝑦(𝜑𝜓)))

Proof of Theorem frege59b
StepHypRef Expression
1 frege58bcor 38697 . 2 (∀𝑦(𝜑𝜓) → ([𝑥 / 𝑦]𝜑 → [𝑥 / 𝑦]𝜓))
2 frege30 38626 . 2 ((∀𝑦(𝜑𝜓) → ([𝑥 / 𝑦]𝜑 → [𝑥 / 𝑦]𝜓)) → ([𝑥 / 𝑦]𝜑 → (¬ [𝑥 / 𝑦]𝜓 → ¬ ∀𝑦(𝜑𝜓))))
31, 2ax-mp 5 1 ([𝑥 / 𝑦]𝜑 → (¬ [𝑥 / 𝑦]𝜓 → ¬ ∀𝑦(𝜑𝜓)))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wal 1628  [wsb 2044
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1869  ax-4 1884  ax-5 1986  ax-6 2052  ax-7 2088  ax-10 2166  ax-12 2194  ax-13 2389  ax-frege1 38584  ax-frege2 38585  ax-frege8 38603  ax-frege28 38624  ax-frege58b 38695
This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-ex 1852  df-nf 1857  df-sb 2045
This theorem is referenced by: (None)
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