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Theorem bj-peirce 32880
Description: Proof of peirce 193 from minimal implicational calculus, the axiomatic definition of disjunction (olc 857, orc 856, jao 945), and Curry's axiom bj-curry 32879. (Contributed by BJ, 4-Apr-2021.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
bj-peirce (((𝜑𝜓) → 𝜑) → 𝜑)

Proof of Theorem bj-peirce
StepHypRef Expression
1 bj-curry 32879 . . 3 (𝜑 ∨ (𝜑𝜓))
2 bj-orim2 32878 . . 3 (((𝜑𝜓) → 𝜑) → ((𝜑 ∨ (𝜑𝜓)) → (𝜑𝜑)))
31, 2mpi 20 . 2 (((𝜑𝜓) → 𝜑) → (𝜑𝜑))
4 pm1.2 889 . 2 ((𝜑𝜑) → 𝜑)
53, 4syl 17 1 (((𝜑𝜓) → 𝜑) → 𝜑)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wo 836
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 197  df-an 383  df-or 837
This theorem is referenced by: (None)
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