Theorem 3exp

Description: Exportation inference. (Contributed by NM, 30-May-1994) (Proof shortened by Wolf Lammen, 22-Jun-2022)

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

Proof

Step	Hyp	Ref	Expression
1		3exp.1	$$⊢\left(\phi \wedge \psi \wedge \chi \right)\to \theta$$
2	1	3expa	$$⊢\left(\left(\phi \wedge \psi \right)\wedge \chi \right)\to \theta$$
3	2	exp31	$$⊢\phi \to \left(\psi \to \left(\chi \to \theta \right)\right)$$