Theorem imp4a

Description: An importation inference. (Contributed by NM, 26-Apr-1994) (Proof shortened by Wolf Lammen, 19-Jul-2021)

	Ref	Expression
Hypothesis	imp4.1	$$⊢\phi \to \left(\psi \to \left(\chi \to \left(\theta \to \tau \right)\right)\right)$$
Assertion	imp4a	$$⊢\phi \to \left(\psi \to \left(\left(\chi \wedge \theta \right)\to \tau \right)\right)$$

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	imp4b	$$⊢\left(\phi \wedge \psi \right)\to \left(\left(\chi \wedge \theta \right)\to \tau \right)$$
3	2	ex	$$⊢\phi \to \left(\psi \to \left(\left(\chi \wedge \theta \right)\to \tau \right)\right)$$