Theorem nic-idel

Description: Inference to remove the trailing term. (Contributed by Jeff Hoffman, 17-Nov-2007) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypothesis	nic-idel.1	$$⊢\left(\phi ⊼\left(\chi ⊼\psi \right)\right)$$
Assertion	nic-idel	$$⊢\left(\phi ⊼\left(\chi ⊼\chi \right)\right)$$

Proof

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