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Mirrors > Home > MPE Home > Th. List > Mathboxes > frege59b | Structured version Visualization version GIF version |
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.) |
Ref | Expression |
---|---|
frege59b | ⊢ ([𝑥 / 𝑦]𝜑 → (¬ [𝑥 / 𝑦]𝜓 → ¬ ∀𝑦(𝜑 → 𝜓))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | frege58bcor 38197 | . 2 ⊢ (∀𝑦(𝜑 → 𝜓) → ([𝑥 / 𝑦]𝜑 → [𝑥 / 𝑦]𝜓)) | |
2 | frege30 38126 | . 2 ⊢ ((∀𝑦(𝜑 → 𝜓) → ([𝑥 / 𝑦]𝜑 → [𝑥 / 𝑦]𝜓)) → ([𝑥 / 𝑦]𝜑 → (¬ [𝑥 / 𝑦]𝜓 → ¬ ∀𝑦(𝜑 → 𝜓)))) | |
3 | 1, 2 | ax-mp 5 | 1 ⊢ ([𝑥 / 𝑦]𝜑 → (¬ [𝑥 / 𝑦]𝜓 → ¬ ∀𝑦(𝜑 → 𝜓))) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 → wi 4 ∀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) |
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