Theorem nic-imp 1440

Description: Inference for nic-mp 1436 using nic-ax 1438 as major premise. (Contributed by Jeff Hoffman, 17-Nov-2007.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypothesis

Ref	Expression
nic-imp.1	⊢ (φ ⊼ (χ ⊼ ψ))

Assertion

Ref	Expression
nic-imp	⊢ ((θ ⊼ χ) ⊼ ((φ ⊼ θ) ⊼ (φ ⊼ θ)))

Proof of Theorem nic-imp

Step	Hyp	Ref	Expression
1		nic-imp.1	. 2 ⊢ (φ ⊼ (χ ⊼ ψ))
2		nic-ax 1438	. 2 ⊢ ((φ ⊼ (χ ⊼ ψ)) ⊼ ((τ ⊼ (τ ⊼ τ)) ⊼ ((θ ⊼ χ) ⊼ ((φ ⊼ θ) ⊼ (φ ⊼ θ)))))
3	1, 2	nic-mp 1436	1 ⊢ ((θ ⊼ χ) ⊼ ((φ ⊼ θ) ⊼ (φ ⊼ θ)))

This proof depends on syntax axioms:   ⊼ wnan 1287

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

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

This theorem is used by:  nic-idlem1  1441  nic-idlem2  1442  nic-isw2  1446  nic-iimp1  1447  nic-idel  1449  nic-ich  1450  nic-idbl  1451  nic-luk1  1456