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Theorem frege10 37631
Description: Result commuting antecedents within an antecedent. Proposition 10 of [Frege1879] p. 36. (Contributed by RP, 24-Dec-2019.) (Proof modification is discouraged.)
Assertion
Ref Expression
frege10 (((𝜑 → (𝜓𝜒)) → 𝜃) → ((𝜓 → (𝜑𝜒)) → 𝜃))

Proof of Theorem frege10
StepHypRef Expression
1 ax-frege8 37620 . 2 ((𝜓 → (𝜑𝜒)) → (𝜑 → (𝜓𝜒)))
2 frege9 37623 . 2 (((𝜓 → (𝜑𝜒)) → (𝜑 → (𝜓𝜒))) → (((𝜑 → (𝜓𝜒)) → 𝜃) → ((𝜓 → (𝜑𝜒)) → 𝜃)))
31, 2ax-mp 5 1 (((𝜑 → (𝜓𝜒)) → 𝜃) → ((𝜓 → (𝜑𝜒)) → 𝜃))
Colors of variables: wff setvar class
Syntax hints:  wi 4
This theorem was proved from axioms:  ax-mp 5  ax-frege1 37601  ax-frege2 37602  ax-frege8 37620
This theorem is referenced by:  frege30  37643
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