Theorem impexp

Description: Import-export theorem. Part of Theorem *4.87 of WhiteheadRussell p. 122. (Contributed by NM, 10-Jan-1993) (Proof shortened by Wolf Lammen, 24-Mar-2013)

	Ref	Expression
Assertion	impexp	$$⊢\left(\left(\phi \wedge \psi \right)\to \chi \right)\leftrightarrow \left(\phi \to \left(\psi \to \chi \right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		pm3.3	$$⊢\left(\left(\phi \wedge \psi \right)\to \chi \right)\to \left(\phi \to \left(\psi \to \chi \right)\right)$$
2		pm3.31	$$⊢\left(\phi \to \left(\psi \to \chi \right)\right)\to \left(\left(\phi \wedge \psi \right)\to \chi \right)$$
3	1 2	impbii	$$⊢\left(\left(\phi \wedge \psi \right)\to \chi \right)\leftrightarrow \left(\phi \to \left(\psi \to \chi \right)\right)$$