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Theorem frege62b 38703
 Description: A kind of Aristotelian inference. This judgement replaces the mode of inference barbara 2701 when the minor premise has a particular context. Proposition 62 of [Frege1879] p. 52. (Contributed by RP, 24-Dec-2019.) (Proof modification is discouraged.)
Assertion
Ref Expression
frege62b ([𝑥 / 𝑦]𝜑 → (∀𝑦(𝜑𝜓) → [𝑥 / 𝑦]𝜓))

Proof of Theorem frege62b
StepHypRef Expression
1 frege58bcor 38699 . 2 (∀𝑦(𝜑𝜓) → ([𝑥 / 𝑦]𝜑 → [𝑥 / 𝑦]𝜓))
2 ax-frege8 38605 . 2 ((∀𝑦(𝜑𝜓) → ([𝑥 / 𝑦]𝜑 → [𝑥 / 𝑦]𝜓)) → ([𝑥 / 𝑦]𝜑 → (∀𝑦(𝜑𝜓) → [𝑥 / 𝑦]𝜓)))
31, 2ax-mp 5 1 ([𝑥 / 𝑦]𝜑 → (∀𝑦(𝜑𝜓) → [𝑥 / 𝑦]𝜓))
 Colors of variables: wff setvar class Syntax hints:   → wi 4  ∀wal 1630  [wsb 2046 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1871  ax-4 1886  ax-5 1988  ax-6 2054  ax-7 2090  ax-10 2168  ax-12 2196  ax-13 2391  ax-frege8 38605  ax-frege58b 38697 This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-ex 1854  df-nf 1859  df-sb 2047 This theorem is referenced by:  frege63b  38704  frege64b  38705
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