Theorem 3impia

Description: Importation to triple conjunction. (Contributed by NM, 13-Jun-2006) (Proof shortened by Wolf Lammen, 21-Jun-2022)

	Ref	Expression
Hypothesis	3impia.1	$$⊢\left(\phi \wedge \psi \right)\to \left(\chi \to \theta \right)$$
Assertion	3impia	$$⊢\left(\phi \wedge \psi \wedge \chi \right)\to \theta$$

Proof

Step	Hyp	Ref	Expression
1		3impia.1	$$⊢\left(\phi \wedge \psi \right)\to \left(\chi \to \theta \right)$$
2	1	expimpd	$$⊢\phi \to \left(\left(\psi \wedge \chi \right)\to \theta \right)$$
3	2	3impib	$$⊢\left(\phi \wedge \psi \wedge \chi \right)\to \theta$$