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Theorem minimp-ax1 1615
Description: Derivation of ax-1 6 from ax-mp 5 and minimp 1613. (Contributed by BJ, 4-Apr-2021.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
minimp-ax1 (𝜑 → (𝜓𝜑))

Proof of Theorem minimp-ax1
StepHypRef Expression
1 minimp-syllsimp 1614 . 2 (((𝜑𝜓) → 𝜑) → (𝜓𝜑))
2 minimp-syllsimp 1614 . 2 ((((𝜑𝜓) → 𝜑) → (𝜓𝜑)) → (𝜑 → (𝜓𝜑)))
31, 2ax-mp 5 1 (𝜑 → (𝜓𝜑))
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-pm2.43  1618
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