Users' Mathboxes Mathbox for Richard Penner < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  frege62b Structured version   Visualization version   GIF version

Theorem frege62b 37024
Description: A kind of Aristotelian inference. This judgement replaces the mode of inference barbara 2550 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 37020 . 2 (∀𝑦(𝜑𝜓) → ([𝑥 / 𝑦]𝜑 → [𝑥 / 𝑦]𝜓))
2 ax-frege8 36926 . 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 1472  [wsb 1866
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1712  ax-4 1727  ax-5 1826  ax-6 1874  ax-7 1921  ax-10 2005  ax-12 2032  ax-13 2232  ax-frege8 36926  ax-frege58b 37018
This theorem depends on definitions:  df-bi 195  df-or 383  df-an 384  df-tru 1477  df-ex 1695  df-nf 1700  df-sb 1867
This theorem is referenced by:  frege63b  37025  frege64b  37026
  Copyright terms: Public domain W3C validator