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Theorem adh-jarrsc 43591
Description: Replacement of a nested antecedent with an outer antecedent. Commuted simplificated form of elimination of a nested antecedent. Also holds intuitionistically. Polish prefix notation: CCCpqrCsCqr . (Contributed by ADH, 10-Nov-2023.) (Proof modification is discouraged.)
Assertion
Ref Expression
adh-jarrsc (((𝜑𝜓) → 𝜒) → (𝜃 → (𝜓𝜒)))

Proof of Theorem adh-jarrsc
StepHypRef Expression
1 jarr 106 . . 3 (((𝜑𝜓) → 𝜒) → (𝜓𝜒))
2 ax-1 6 . . 3 ((((𝜑𝜓) → 𝜒) → (𝜓𝜒)) → (𝜃 → (((𝜑𝜓) → 𝜒) → (𝜓𝜒))))
31, 2ax-mp 5 . 2 (𝜃 → (((𝜑𝜓) → 𝜒) → (𝜓𝜒)))
4 pm2.04 90 . 2 ((𝜃 → (((𝜑𝜓) → 𝜒) → (𝜓𝜒))) → (((𝜑𝜓) → 𝜒) → (𝜃 → (𝜓𝜒))))
53, 4ax-mp 5 1 (((𝜑𝜓) → 𝜒) → (𝜃 → (𝜓𝜒)))
Colors of variables: wff setvar class
Syntax hints:  wi 4
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7
This theorem is referenced by:  adh-minim  43592
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