Theorem nic-idel 1609

Description: Inference to remove the trailing term. (Contributed by Jeff Hoffman, 17-Nov-2007.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypothesis

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

Assertion

Ref	Expression
nic-idel	⊢ (𝜑 ⊼ (𝜒 ⊼ 𝜒))

Proof of Theorem nic-idel

Step	Hyp	Ref	Expression
1		nic-id 1603	. . 3 ⊢ (𝜒 ⊼ (𝜒 ⊼ 𝜒))
2	1	nic-isw1 1605	. 2 ⊢ ((𝜒 ⊼ 𝜒) ⊼ 𝜒)
3		nic-idel.1	. . 3 ⊢ (𝜑 ⊼ (𝜒 ⊼ 𝜓))
4	3	nic-imp 1600	. 2 ⊢ (((𝜒 ⊼ 𝜒) ⊼ 𝜒) ⊼ ((𝜑 ⊼ (𝜒 ⊼ 𝜒)) ⊼ (𝜑 ⊼ (𝜒 ⊼ 𝜒))))
5	2, 4	nic-mp 1596	1 ⊢ (𝜑 ⊼ (𝜒 ⊼ 𝜒))

Syntax hints:   ⊼ wnan 1447

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 197  df-an 386  df-nan 1448

This theorem is referenced by:  nic-bi1  1613  nic-bi2  1614  nic-luk1  1616