Theorem nic-id 1443

Description: Theorem id 19 expressed with ⊼. (Contributed by Jeff Hoffman, 17-Nov-2007.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
nic-id	⊢ (τ ⊼ (τ ⊼ τ))

Proof of Theorem nic-id

Step	Hyp	Ref	Expression
1		nic-ax 1438	. . 3 ⊢ ((ψ ⊼ (ψ ⊼ ψ)) ⊼ ((θ ⊼ (θ ⊼ θ)) ⊼ ((φ ⊼ ψ) ⊼ ((ψ ⊼ φ) ⊼ (ψ ⊼ φ)))))
2	1	nic-idlem2 1442	. 2 ⊢ ((((φ ⊼ ψ) ⊼ ((ψ ⊼ φ) ⊼ (ψ ⊼ φ))) ⊼ (χ ⊼ (χ ⊼ χ))) ⊼ (ψ ⊼ (ψ ⊼ ψ)))
3		nic-idlem1 1441	. . 3 ⊢ (((χ ⊼ (χ ⊼ χ)) ⊼ (τ ⊼ (τ ⊼ τ))) ⊼ ((((φ ⊼ ψ) ⊼ ((ψ ⊼ φ) ⊼ (ψ ⊼ φ))) ⊼ (χ ⊼ (χ ⊼ χ))) ⊼ (((φ ⊼ ψ) ⊼ ((ψ ⊼ φ) ⊼ (ψ ⊼ φ))) ⊼ (χ ⊼ (χ ⊼ χ)))))
4	3	nic-idlem2 1442	. 2 ⊢ (((((φ ⊼ ψ) ⊼ ((ψ ⊼ φ) ⊼ (ψ ⊼ φ))) ⊼ (χ ⊼ (χ ⊼ χ))) ⊼ (ψ ⊼ (ψ ⊼ ψ))) ⊼ ((χ ⊼ (χ ⊼ χ)) ⊼ (τ ⊼ (τ ⊼ τ))))
5	2, 4	nic-mp 1436	1 ⊢ (τ ⊼ (τ ⊼ τ))

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-swap  1444  nic-idel  1449  nic-bi1  1453  nic-bi2  1454  nic-luk2  1457  nic-luk3  1458