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Theorem frege59b 38515
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 38424 incorrectly referenced where frege30 38443 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 38514 . 2 (∀𝑦(𝜑𝜓) → ([𝑥 / 𝑦]𝜑 → [𝑥 / 𝑦]𝜓))
2 frege30 38443 . 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 1521  [wsb 1937
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1762  ax-4 1777  ax-5 1879  ax-6 1945  ax-7 1981  ax-10 2059  ax-12 2087  ax-13 2282  ax-frege1 38401  ax-frege2 38402  ax-frege8 38420  ax-frege28 38441  ax-frege58b 38512
This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-ex 1745  df-nf 1750  df-sb 1938
This theorem is referenced by: (None)
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