Theorem 3expia

Description: Exportation from triple conjunction. (Contributed by NM, 19-May-2007) (Proof shortened by Wolf Lammen, 22-Jun-2022)

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

Proof

Step	Hyp	Ref	Expression
1		3exp.1	$$⊢\left(\phi \wedge \psi \wedge \chi \right)\to \theta$$
2	1	3expb	$$⊢\left(\phi \wedge \left(\psi \wedge \chi \right)\right)\to \theta$$
3	2	expr	$$⊢\left(\phi \wedge \psi \right)\to \left(\chi \to \theta \right)$$