Theorem dfor2 400

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		pm2.62 398	. 2 ⊢ ((φ ∨ ψ) → ((φ → ψ) → ψ))
2		pm2.68 399	. 2 ⊢ (((φ → ψ) → ψ) → (φ ∨ ψ))
3	1, 2	impbii 180	1 ⊢ ((φ ∨ ψ) ↔ ((φ → ψ) → ψ))

This proof depends on syntax axioms:   → wi 4   ↔ wb 176   ∨ wo 357

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

This proof depends on definitions:  df-bi 177  df-or 359

This theorem is used by:  imimorb  847