Theorem exp43

Description: An exportation inference. (Contributed by NM, 26-Apr-1994)

	Ref	Expression
Hypothesis	exp43.1	$$⊢\left(\left(\phi \wedge \psi \right)\wedge \left(\chi \wedge \theta \right)\right)\to \tau$$
Assertion	exp43	$$⊢\phi \to \left(\psi \to \left(\chi \to \left(\theta \to \tau \right)\right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		exp43.1	$$⊢\left(\left(\phi \wedge \psi \right)\wedge \left(\chi \wedge \theta \right)\right)\to \tau$$
2	1	ex	$$⊢\left(\phi \wedge \psi \right)\to \left(\left(\chi \wedge \theta \right)\to \tau \right)$$
3	2	exp4b	$$⊢\phi \to \left(\psi \to \left(\chi \to \left(\theta \to \tau \right)\right)\right)$$