Theorem exp4b

Description: An exportation inference. (Contributed by NM, 26-Apr-1994) (Proof shortened by Wolf Lammen, 23-Nov-2012) Shorten exp4a . (Revised by Wolf Lammen, 20-Jul-2021)

	Ref	Expression
Hypothesis	exp4b.1	$$⊢\left(\phi \wedge \psi \right)\to \left(\left(\chi \wedge \theta \right)\to \tau \right)$$
Assertion	exp4b	$$⊢\phi \to \left(\psi \to \left(\chi \to \left(\theta \to \tau \right)\right)\right)$$

Proof

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