Theorem nic-iimp1 1447

Description: Inference version of nic-imp 1440 using right-handed term. (Contributed by Jeff Hoffman, 17-Nov-2007.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
nic-iimp1.1	⊢ (φ ⊼ (χ ⊼ ψ))
nic-iimp1.2	⊢ (θ ⊼ χ)

Assertion

Ref	Expression
nic-iimp1	⊢ (θ ⊼ φ)

Proof of Theorem nic-iimp1

Step	Hyp	Ref	Expression
1		nic-iimp1.2	. . 3 ⊢ (θ ⊼ χ)
2		nic-iimp1.1	. . . 4 ⊢ (φ ⊼ (χ ⊼ ψ))
3	2	nic-imp 1440	. . 3 ⊢ ((θ ⊼ χ) ⊼ ((φ ⊼ θ) ⊼ (φ ⊼ θ)))
4	1, 3	nic-mp 1436	. 2 ⊢ (φ ⊼ θ)
5	4	nic-isw1 1445	1 ⊢ (θ ⊼ φ)

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-iimp2  1448  nic-bi1  1453  nic-bi2  1454  nic-luk2  1457  nic-luk3  1458