Theorem 3imp

Description: Importation inference. (Contributed by NM, 8-Apr-1994) (Proof shortened by Wolf Lammen, 20-Jun-2022)

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

Proof

Step	Hyp	Ref	Expression
1		3imp.1	$$⊢\phi \to \left(\psi \to \left(\chi \to \theta \right)\right)$$
2	1	imp31	$$⊢\left(\left(\phi \wedge \psi \right)\wedge \chi \right)\to \theta$$
3	2	3impa	$$⊢\left(\phi \wedge \psi \wedge \chi \right)\to \theta$$