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Theorem minimp 1550
Description: A single axiom for minimal implicational calculus, due to Meredith. Other single axioms of the same length are known, but it is thought to be the minimal length. (Contributed by BJ, 4-Apr-2021.)
Assertion
Ref Expression
minimp (𝜑 → ((𝜓𝜒) → (((𝜃𝜓) → (𝜒𝜏)) → (𝜓𝜏))))

Proof of Theorem minimp
StepHypRef Expression
1 jarr 103 . . . 4 (((𝜃𝜓) → (𝜒𝜏)) → (𝜓 → (𝜒𝜏)))
21a2d 29 . . 3 (((𝜃𝜓) → (𝜒𝜏)) → ((𝜓𝜒) → (𝜓𝜏)))
32com12 32 . 2 ((𝜓𝜒) → (((𝜃𝜓) → (𝜒𝜏)) → (𝜓𝜏)))
43a1i 11 1 (𝜑 → ((𝜓𝜒) → (((𝜃𝜓) → (𝜒𝜏)) → (𝜓𝜏))))
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:  minimp-sylsimp  1551  minimp-ax2c  1553
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