Theorem nic-idlem1 1441

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

Assertion

Ref	Expression
nic-idlem1	⊢ ((θ ⊼ (τ ⊼ (τ ⊼ τ))) ⊼ (((φ ⊼ (χ ⊼ ψ)) ⊼ θ) ⊼ ((φ ⊼ (χ ⊼ ψ)) ⊼ θ)))

Proof of Theorem nic-idlem1

Step	Hyp	Ref	Expression
1		nic-ax 1438	. 2 ⊢ ((φ ⊼ (χ ⊼ ψ)) ⊼ ((τ ⊼ (τ ⊼ τ)) ⊼ ((φ ⊼ χ) ⊼ ((φ ⊼ φ) ⊼ (φ ⊼ φ)))))
2	1	nic-imp 1440	1 ⊢ ((θ ⊼ (τ ⊼ (τ ⊼ τ))) ⊼ (((φ ⊼ (χ ⊼ ψ)) ⊼ θ) ⊼ ((φ ⊼ (χ ⊼ ψ)) ⊼ θ)))

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