Theorem 3imp31

Description: The importation inference 3imp with commutation of the first and third conjuncts of the assertion relative to the hypothesis. (Contributed by Alan Sare, 11-Sep-2016)

	Ref	Expression
Hypothesis	3imp.1	$$⊢\phi \to \left(\psi \to \left(\chi \to \theta \right)\right)$$
Assertion	3imp31	$$⊢\left(\chi \wedge \psi \wedge \phi \right)\to \theta$$

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	3imp	$$⊢\left(\chi \wedge \psi \wedge \phi \right)\to \theta$$