Theorem nic-iimp1

Description: Inference version of nic-imp using right-handed term. (Contributed by Jeff Hoffman, 17-Nov-2007) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	nic-iimp1.1	$$⊢\left(\phi ⊼\left(\chi ⊼\psi \right)\right)$$
	nic-iimp1.2	$$⊢\left(\theta ⊼\chi \right)$$
Assertion	nic-iimp1	$$⊢\left(\theta ⊼\phi \right)$$

Proof

Step	Hyp	Ref	Expression
1		nic-iimp1.1	$$⊢\left(\phi ⊼\left(\chi ⊼\psi \right)\right)$$
2		nic-iimp1.2	$$⊢\left(\theta ⊼\chi \right)$$
3	1	nic-imp	$$⊢\left(\left(\theta ⊼\chi \right)⊼\left(\left(\phi ⊼\theta \right)⊼\left(\phi ⊼\theta \right)\right)\right)$$
4	2 3	nic-mp	$$⊢\left(\phi ⊼\theta \right)$$
5	4	nic-isw1	$$⊢\left(\theta ⊼\phi \right)$$