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	⊢ ( ( 𝜑 ⊼ 𝜓 ) ⊼ ( 𝜒 ⊼ 𝜒 ) )
	nic-iimp2.2	⊢ ( 𝜃 ⊼ 𝜑 )
Assertion	nic-iimp2	⊢ ( 𝜃 ⊼ ( 𝜒 ⊼ 𝜒 ) )

Proof

Step	Hyp	Ref	Expression
1		nic-iimp2.1	⊢ ( ( 𝜑 ⊼ 𝜓 ) ⊼ ( 𝜒 ⊼ 𝜒 ) )
2		nic-iimp2.2	⊢ ( 𝜃 ⊼ 𝜑 )
3	1	nic-isw1	⊢ ( ( 𝜒 ⊼ 𝜒 ) ⊼ ( 𝜑 ⊼ 𝜓 ) )
4	3 2	nic-iimp1	⊢ ( 𝜃 ⊼ ( 𝜒 ⊼ 𝜒 ) )