Theorem nic-isw1

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

	Ref	Expression
Hypothesis	nic-isw1.1	$$⊢\left(\theta ⊼\phi \right)$$
Assertion	nic-isw1	$$⊢\left(\phi ⊼\theta \right)$$

Proof

Step	Hyp	Ref	Expression
1		nic-isw1.1	$$⊢\left(\theta ⊼\phi \right)$$
2		nic-swap	$$⊢\left(\left(\theta ⊼\phi \right)⊼\left(\left(\phi ⊼\theta \right)⊼\left(\phi ⊼\theta \right)\right)\right)$$
3	1 2	nic-mp	$$⊢\left(\phi ⊼\theta \right)$$