Theorem nic-idlem1 1679

Description: Lemma for nic-id 1681. (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 1676	. 2 ⊢ ((𝜑 ⊼ (𝜒 ⊼ 𝜓)) ⊼ ((𝜏 ⊼ (𝜏 ⊼ 𝜏)) ⊼ ((𝜑 ⊼ 𝜒) ⊼ ((𝜑 ⊼ 𝜑) ⊼ (𝜑 ⊼ 𝜑)))))
2	1	nic-imp 1678	1 ⊢ ((𝜃 ⊼ (𝜏 ⊼ (𝜏 ⊼ 𝜏))) ⊼ (((𝜑 ⊼ (𝜒 ⊼ 𝜓)) ⊼ 𝜃) ⊼ ((𝜑 ⊼ (𝜒 ⊼ 𝜓)) ⊼ 𝜃)))

Syntax hints:   ⊼ wnan 1486

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 206  df-an 397  df-nan 1487

This theorem is referenced by:  nic-id  1681