Theorem imp4d

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

	Ref	Expression
Hypothesis	imp4.1	$$⊢\phi \to \left(\psi \to \left(\chi \to \left(\theta \to \tau \right)\right)\right)$$
Assertion	imp4d	$$⊢\phi \to \left(\left(\psi \wedge \left(\chi \wedge \theta \right)\right)\to \tau \right)$$

Proof

Step	Hyp	Ref	Expression
1		imp4.1	$$⊢\phi \to \left(\psi \to \left(\chi \to \left(\theta \to \tau \right)\right)\right)$$
2	1	imp4a	$$⊢\phi \to \left(\psi \to \left(\left(\chi \wedge \theta \right)\to \tau \right)\right)$$
3	2	impd	$$⊢\phi \to \left(\left(\psi \wedge \left(\chi \wedge \theta \right)\right)\to \tau \right)$$