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Theorem curryax 891
Description: A non-intuitionistic positive statement, sometimes called a paradox of material implication. Sometimes called Curry's axiom. Similar to exmid 892 (obtained by substituting for 𝜓) but positive. For another non-intuitionistic positive statement, see peirce 201. (Contributed by BJ, 4-Apr-2021.)
Assertion
Ref Expression
curryax (𝜑 ∨ (𝜑𝜓))

Proof of Theorem curryax
StepHypRef Expression
1 pm2.21 123 . 2 𝜑 → (𝜑𝜓))
21orri 859 1 (𝜑 ∨ (𝜑𝜓))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wo 844
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 206  df-or 845
This theorem is referenced by:  reuprg  4640  tsim2  36275
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