Theorem nic-iimp2 1448

Description: Inference version of nic-imp 1440 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 1445	. 2 ⊢ ((χ ⊼ χ) ⊼ (φ ⊼ ψ))
3		nic-iimp2.2	. 2 ⊢ (θ ⊼ φ)
4	2, 3	nic-iimp1 1447	1 ⊢ (θ ⊼ (χ ⊼ χ))

Syntax hints:   ⊼ wnan 1287

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 177  df-an 360  df-nan 1288

This theorem is referenced by:  nic-luk3  1458