Theorem dfor2 902

Description: Logical 'or' expressed in terms of implication only. Theorem *5.25 of [WhiteheadRussell] p. 124. (Contributed by NM, 12-Aug-2004.) (Proof shortened by Wolf Lammen, 20-Oct-2012.)

Assertion

Ref	Expression
dfor2	⊢ ((𝜑 ∨ 𝜓) ↔ ((𝜑 → 𝜓) → 𝜓))

Proof of Theorem dfor2

Step	Hyp	Ref	Expression
1		pm2.62 900	. 2 ⊢ ((𝜑 ∨ 𝜓) → ((𝜑 → 𝜓) → 𝜓))
2		pm2.68 901	. 2 ⊢ (((𝜑 → 𝜓) → 𝜓) → (𝜑 ∨ 𝜓))
3	1, 2	impbii 209	1 ⊢ ((𝜑 ∨ 𝜓) ↔ ((𝜑 → 𝜓) → 𝜓))

Syntax hints:   → wi 4   ↔ wb 206   ∨ wo 848

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 207  df-or 849

This theorem is referenced by:  imimorb  953  ifpim23g  43508