Theorem dfor2

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)

	Ref	Expression
Assertion	dfor2	$$⊢\left(\phi \vee \psi \right)\leftrightarrow \left(\left(\phi \to \psi \right)\to \psi \right)$$

Proof

Step	Hyp	Ref	Expression
1		pm2.62	$$⊢\left(\phi \vee \psi \right)\to \left(\left(\phi \to \psi \right)\to \psi \right)$$
2		pm2.68	$$⊢\left(\left(\phi \to \psi \right)\to \psi \right)\to \left(\phi \vee \psi \right)$$
3	1 2	impbii	$$⊢\left(\phi \vee \psi \right)\leftrightarrow \left(\left(\phi \to \psi \right)\to \psi \right)$$