MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  curryax Structured version   Visualization version   GIF version

Theorem curryax 890
Description: A non-intuitionistic positive statement, sometimes called a paradox of material implication. Sometimes called Curry's axiom. Similar to exmid 891 (obtained by substituting for 𝜓) but positive. For another non-intuitionistic positive statement, see peirce 204. (Contributed by BJ, 4-Apr-2021.)
Ref Expression
curryax (𝜑 ∨ (𝜑𝜓))

Proof of Theorem curryax
StepHypRef Expression
1 pm2.21 123 . 2 𝜑 → (𝜑𝜓))
21orri 858 1 (𝜑 ∨ (𝜑𝜓))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wo 843
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 209  df-or 844
This theorem is referenced by:  reuprg  4615  tsim2  35445
  Copyright terms: Public domain W3C validator