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Theorem minimp 1623
 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. Among single axioms of this length, it is the one with simplest antecedents (i.e., in the corresponding ordering of binary trees which first compares left subtrees, it is the first one). (Contributed by BJ, 4-Apr-2021.)
Assertion
Ref Expression
minimp (𝜑 → ((𝜓𝜒) → (((𝜃𝜓) → (𝜒𝜏)) → (𝜓𝜏))))

Proof of Theorem minimp
StepHypRef Expression
1 jarr 106 . . . 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-syllsimp  1624  minimp-ax2c  1626
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