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Theorem frege59b 43922
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 43831 incorrectly referenced where frege30 43850 is in the original. (Contributed by RP, 24-Dec-2019.) (Proof modification is discouraged.)

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

Proof of Theorem frege59b
StepHypRef Expression
1 frege58bcor 43921 . 2 (∀𝑥(𝜑𝜓) → ([𝑦 / 𝑥]𝜑 → [𝑦 / 𝑥]𝜓))
2 frege30 43850 . 2 ((∀𝑥(𝜑𝜓) → ([𝑦 / 𝑥]𝜑 → [𝑦 / 𝑥]𝜓)) → ([𝑦 / 𝑥]𝜑 → (¬ [𝑦 / 𝑥]𝜓 → ¬ ∀𝑥(𝜑𝜓))))
31, 2ax-mp 5 1 ([𝑦 / 𝑥]𝜑 → (¬ [𝑦 / 𝑥]𝜓 → ¬ ∀𝑥(𝜑𝜓)))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wal 1537  [wsb 2063
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1794  ax-4 1808  ax-5 1909  ax-6 1966  ax-7 2006  ax-10 2140  ax-12 2176  ax-frege1 43808  ax-frege2 43809  ax-frege8 43827  ax-frege28 43848  ax-frege58b 43919
This theorem depends on definitions:  df-bi 207  df-an 396  df-ex 1779  df-nf 1783  df-sb 2064
This theorem is referenced by: (None)
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