Mathbox for Richard Penner < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  frege62a Structured version   Visualization version   GIF version

Theorem frege62a 39015
 Description: A kind of Aristotelian inference. This judgement replaces the mode of inference barbara 2747 when the minor premise has a particular context. Proposition 62 of [Frege1879] p. 52. (Contributed by RP, 17-Apr-2020.) (Proof modification is discouraged.)
Assertion
Ref Expression
frege62a (if-(𝜑, 𝜓, 𝜃) → (((𝜓𝜒) ∧ (𝜃𝜏)) → if-(𝜑, 𝜒, 𝜏)))

Proof of Theorem frege62a
StepHypRef Expression
1 frege58acor 39011 . 2 (((𝜓𝜒) ∧ (𝜃𝜏)) → (if-(𝜑, 𝜓, 𝜃) → if-(𝜑, 𝜒, 𝜏)))
2 ax-frege8 38944 . 2 ((((𝜓𝜒) ∧ (𝜃𝜏)) → (if-(𝜑, 𝜓, 𝜃) → if-(𝜑, 𝜒, 𝜏))) → (if-(𝜑, 𝜓, 𝜃) → (((𝜓𝜒) ∧ (𝜃𝜏)) → if-(𝜑, 𝜒, 𝜏))))
31, 2ax-mp 5 1 (if-(𝜑, 𝜓, 𝜃) → (((𝜓𝜒) ∧ (𝜃𝜏)) → if-(𝜑, 𝜒, 𝜏)))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∧ wa 386  if-wif 1091 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-frege8 38944  ax-frege58a 39010 This theorem depends on definitions:  df-bi 199  df-an 387  df-or 881  df-ifp 1092 This theorem is referenced by:  frege63a  39016  frege64a  39017
 Copyright terms: Public domain W3C validator