Theorem dfor2 915

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		pm2.62 913	. 2 ⊢ ((𝜑 ∨ 𝜓) → ((𝜑 → 𝜓) → 𝜓))
2		pm2.68 914	. 2 ⊢ (((𝜑 → 𝜓) → 𝜓) → (𝜑 ∨ 𝜓))
3	1, 2	impbii 212	1 ⊢ ((𝜑 ∨ 𝜓) ↔ ((𝜑 → 𝜓) → 𝜓))

This proof depends on syntax axioms:   → wi 4   ↔ wb 209   ∨ wo 861

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 210  df-or 862

This theorem is used by:  imimorb  965  ifpim23g  44262