Theorem bj-curry 32542

Description: A non-intuitionistic positive statement, sometimes called a paradox of material implication. Sometimes called Curry's axiom. (Contributed by BJ, 4-Apr-2021.)

Assertion

Ref	Expression
bj-curry	⊢ (𝜑 ∨ (𝜑 → 𝜓))

Proof of Theorem bj-curry

Step	Hyp	Ref	Expression
1		pm2.21 120	. 2 ⊢ (¬ 𝜑 → (𝜑 → 𝜓))
2	1	orri 391	1 ⊢ (𝜑 ∨ (𝜑 → 𝜓))

Syntax hints:   → wi 4   ∨ wo 383

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-or 385

This theorem is referenced by:  bj-peirce  32543