Theorem pm3.31

Description: Theorem *3.31 (Imp) of WhiteheadRussell p. 112. (Contributed by NM, 3-Jan-2005) (Proof shortened by Wolf Lammen, 24-Mar-2013)

	Ref	Expression
Assertion	pm3.31	$$⊢\left(\phi \to \left(\psi \to \chi \right)\right)\to \left(\left(\phi \wedge \psi \right)\to \chi \right)$$

Proof

Step	Hyp	Ref	Expression
1		id	$$⊢\left(\phi \to \left(\psi \to \chi \right)\right)\to \left(\phi \to \left(\psi \to \chi \right)\right)$$
2	1	impd	$$⊢\left(\phi \to \left(\psi \to \chi \right)\right)\to \left(\left(\phi \wedge \psi \right)\to \chi \right)$$