Theorem impd

Description: Importation deduction. (Contributed by NM, 31-Mar-1994)

	Ref	Expression
Hypothesis	impd.1	$$⊢\phi \to \left(\psi \to \left(\chi \to \theta \right)\right)$$
Assertion	impd	$$⊢\phi \to \left(\left(\psi \wedge \chi \right)\to \theta \right)$$

Proof

Step	Hyp	Ref	Expression
1		impd.1	$$⊢\phi \to \left(\psi \to \left(\chi \to \theta \right)\right)$$
2	1	com3l	$$⊢\psi \to \left(\chi \to \left(\phi \to \theta \right)\right)$$
3	2	imp	$$⊢\left(\psi \wedge \chi \right)\to \left(\phi \to \theta \right)$$
4	3	com12	$$⊢\phi \to \left(\left(\psi \wedge \chi \right)\to \theta \right)$$