Theorem impancom

Description: Mixed importation/commutation inference. (Contributed by NM, 22-Jun-2013)

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

Proof

Step	Hyp	Ref	Expression
1		impancom.1	$$⊢\left(\phi \wedge \psi \right)\to \left(\chi \to \theta \right)$$
2	1	ex	$$⊢\phi \to \left(\psi \to \left(\chi \to \theta \right)\right)$$
3	2	com23	$$⊢\phi \to \left(\chi \to \left(\psi \to \theta \right)\right)$$
4	3	imp	$$⊢\left(\phi \wedge \chi \right)\to \left(\psi \to \theta \right)$$