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Theorem frege62a 38491
Description: A kind of Aristotelian inference. This judgement replaces the mode of inference barbara 2592 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 38487 . 2 (((𝜓𝜒) ∧ (𝜃𝜏)) → (if-(𝜑, 𝜓, 𝜃) → if-(𝜑, 𝜒, 𝜏)))
2 ax-frege8 38420 . 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 383  if-wif 1032
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-frege8 38420  ax-frege58a 38486
This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-ifp 1033
This theorem is referenced by:  frege63a  38492  frege64a  38493
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