Theorem pm5.41

Description: Theorem *5.41 of WhiteheadRussell p. 125. (Contributed by NM, 3-Jan-2005) (Proof shortened by Wolf Lammen, 12-Oct-2012)

	Ref	Expression
Assertion	pm5.41	$$⊢\left(\left(\phi \to \psi \right)\to \left(\phi \to \chi \right)\right)\leftrightarrow \left(\phi \to \left(\psi \to \chi \right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		imdi	$$⊢\left(\phi \to \left(\psi \to \chi \right)\right)\leftrightarrow \left(\left(\phi \to \psi \right)\to \left(\phi \to \chi \right)\right)$$
2	1	bicomi	$$⊢\left(\left(\phi \to \psi \right)\to \left(\phi \to \chi \right)\right)\leftrightarrow \left(\phi \to \left(\psi \to \chi \right)\right)$$