Theorem 3imp21

Description: The importation inference 3imp with commutation of the first and second conjuncts of the assertion relative to the hypothesis. (Contributed by Alan Sare, 11-Sep-2016) (Revised to shorten 3com12 by Wolf Lammen, 23-Jun-2022.)

	Ref	Expression
Hypothesis	3imp.1	$$⊢\phi \to \left(\psi \to \left(\chi \to \theta \right)\right)$$
Assertion	3imp21	$$⊢\left(\psi \wedge \phi \wedge \chi \right)\to \theta$$

Proof

Step	Hyp	Ref	Expression
1		3imp.1	$$⊢\phi \to \left(\psi \to \left(\chi \to \theta \right)\right)$$
2	1	com13	$$⊢\chi \to \left(\psi \to \left(\phi \to \theta \right)\right)$$
3	2	3imp231	$$⊢\left(\psi \wedge \phi \wedge \chi \right)\to \theta$$