Theorem nic-iimp2 1716

Description: Inference version of nic-imp 1708 using left-handed term. (Contributed by Jeff Hoffman, 17-Nov-2007.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
nic-iimp2.1	⊢ ((𝜑 ⊼ 𝜓) ⊼ (𝜒 ⊼ 𝜒))
nic-iimp2.2	⊢ (𝜃 ⊼ 𝜑)

Assertion

Ref	Expression
nic-iimp2	⊢ (𝜃 ⊼ (𝜒 ⊼ 𝜒))

Proof of Theorem nic-iimp2

Step	Hyp	Ref	Expression
1		nic-iimp2.1	. . 3 ⊢ ((𝜑 ⊼ 𝜓) ⊼ (𝜒 ⊼ 𝜒))
2	1	nic-isw1 1713	. 2 ⊢ ((𝜒 ⊼ 𝜒) ⊼ (𝜑 ⊼ 𝜓))
3		nic-iimp2.2	. 2 ⊢ (𝜃 ⊼ 𝜑)
4	2, 3	nic-iimp1 1715	1 ⊢ (𝜃 ⊼ (𝜒 ⊼ 𝜒))

This proof depends on syntax axioms:   ⊼ wnan 1521

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 210  df-an 402  df-nan 1522

This theorem is used by:  nic-luk3  1726