Theorem pm2.86

Description: Converse of axiom ax-2 . Theorem *2.86 of WhiteheadRussell p. 108. (Contributed by NM, 25-Apr-1994) (Proof shortened by Wolf Lammen, 3-Apr-2013)

	Ref	Expression
Assertion	pm2.86	$$⊢\left(\left(\phi \to \psi \right)\to \left(\phi \to \chi \right)\right)\to \left(\phi \to \left(\psi \to \chi \right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		id	$$⊢\left(\left(\phi \to \psi \right)\to \left(\phi \to \chi \right)\right)\to \left(\left(\phi \to \psi \right)\to \left(\phi \to \chi \right)\right)$$
2	1	pm2.86d	$$⊢\left(\left(\phi \to \psi \right)\to \left(\phi \to \chi \right)\right)\to \left(\phi \to \left(\psi \to \chi \right)\right)$$