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	⊢ ( 𝜑 ⊼ ( 𝜒 ⊼ 𝜓 ) )
	nic-iimp1.2	⊢ ( 𝜃 ⊼ 𝜒 )
Assertion	nic-iimp1	⊢ ( 𝜃 ⊼ 𝜑 )

Proof

Step	Hyp	Ref	Expression
1		nic-iimp1.1	⊢ ( 𝜑 ⊼ ( 𝜒 ⊼ 𝜓 ) )
2		nic-iimp1.2	⊢ ( 𝜃 ⊼ 𝜒 )
3	1	nic-imp	⊢ ( ( 𝜃 ⊼ 𝜒 ) ⊼ ( ( 𝜑 ⊼ 𝜃 ) ⊼ ( 𝜑 ⊼ 𝜃 ) ) )
4	2 3	nic-mp	⊢ ( 𝜑 ⊼ 𝜃 )
5	4	nic-isw1	⊢ ( 𝜃 ⊼ 𝜑 )