Theorem nic-idlem2 1442

Description: Lemma for nic-id 1443. Inference used by nic-id 1443. (Contributed by Jeff Hoffman, 17-Nov-2007.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypothesis

Ref	Expression
nic-idlem2.1	⊢ (η ⊼ ((φ ⊼ (χ ⊼ ψ)) ⊼ θ))

Assertion

Ref	Expression
nic-idlem2	⊢ ((θ ⊼ (τ ⊼ (τ ⊼ τ))) ⊼ η)

Proof of Theorem nic-idlem2

Step	Hyp	Ref	Expression
1		nic-idlem2.1	. 2 ⊢ (η ⊼ ((φ ⊼ (χ ⊼ ψ)) ⊼ θ))
2		nic-ax 1438	. . . 4 ⊢ ((φ ⊼ (χ ⊼ ψ)) ⊼ ((τ ⊼ (τ ⊼ τ)) ⊼ ((φ ⊼ χ) ⊼ ((φ ⊼ φ) ⊼ (φ ⊼ φ)))))
3	2	nic-imp 1440	. . 3 ⊢ ((θ ⊼ (τ ⊼ (τ ⊼ τ))) ⊼ (((φ ⊼ (χ ⊼ ψ)) ⊼ θ) ⊼ ((φ ⊼ (χ ⊼ ψ)) ⊼ θ)))
4	3	nic-imp 1440	. 2 ⊢ ((η ⊼ ((φ ⊼ (χ ⊼ ψ)) ⊼ θ)) ⊼ (((θ ⊼ (τ ⊼ (τ ⊼ τ))) ⊼ η) ⊼ ((θ ⊼ (τ ⊼ (τ ⊼ τ))) ⊼ η)))
5	1, 4	nic-mp 1436	1 ⊢ ((θ ⊼ (τ ⊼ (τ ⊼ τ))) ⊼ η)

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-id  1443