Theorem nic-iimp2

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

	Ref	Expression
Hypotheses	nic-iimp2.1	$$⊢\left(\left(\phi ⊼\psi \right)⊼\left(\chi ⊼\chi \right)\right)$$
	nic-iimp2.2	$$⊢\left(\theta ⊼\phi \right)$$
Assertion	nic-iimp2	$$⊢\left(\theta ⊼\left(\chi ⊼\chi \right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		nic-iimp2.1	$$⊢\left(\left(\phi ⊼\psi \right)⊼\left(\chi ⊼\chi \right)\right)$$
2		nic-iimp2.2	$$⊢\left(\theta ⊼\phi \right)$$
3	1	nic-isw1	$$⊢\left(\left(\chi ⊼\chi \right)⊼\left(\phi ⊼\psi \right)\right)$$
4	3 2	nic-iimp1	$$⊢\left(\theta ⊼\left(\chi ⊼\chi \right)\right)$$