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Theorem bj-orim2 31545
Description: Proof of orim2 881 from the axiomatic definition of disjunction (olc 397, orc 398, jao 532) and minimal implicational calculus. (Contributed by BJ, 4-Apr-2021.) (Proof modification is discouraged.)
Assertion
Ref Expression
bj-orim2 ((𝜑𝜓) → ((𝜒𝜑) → (𝜒𝜓)))

Proof of Theorem bj-orim2
StepHypRef Expression
1 orc 398 . 2 (𝜒 → (𝜒𝜓))
2 olc 397 . . 3 (𝜓 → (𝜒𝜓))
32imim2i 16 . 2 ((𝜑𝜓) → (𝜑 → (𝜒𝜓)))
4 jao 532 . 2 ((𝜒 → (𝜒𝜓)) → ((𝜑 → (𝜒𝜓)) → ((𝜒𝜑) → (𝜒𝜓))))
51, 3, 4mpsyl 65 1 ((𝜑𝜓) → ((𝜒𝜑) → (𝜒𝜓)))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wo 381
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 195  df-or 383  df-an 384
This theorem is referenced by:  bj-peirce  31547
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