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	⊢ ( 𝜃 ⊼ 𝜑 )
Assertion	nic-isw1	⊢ ( 𝜑 ⊼ 𝜃 )

Proof

Step	Hyp	Ref	Expression
1		nic-isw1.1	⊢ ( 𝜃 ⊼ 𝜑 )
2		nic-swap	⊢ ( ( 𝜃 ⊼ 𝜑 ) ⊼ ( ( 𝜑 ⊼ 𝜃 ) ⊼ ( 𝜑 ⊼ 𝜃 ) ) )
3	1 2	nic-mp	⊢ ( 𝜑 ⊼ 𝜃 )