Theorem nic-ich 1450

Description: Chained inference. (Contributed by Jeff Hoffman, 17-Nov-2007.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
nic-ich.1	⊢ (φ ⊼ (ψ ⊼ ψ))
nic-ich.2	⊢ (ψ ⊼ (χ ⊼ χ))

Assertion

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

Proof of Theorem nic-ich

Step	Hyp	Ref	Expression
1		nic-ich.2	. . 3 ⊢ (ψ ⊼ (χ ⊼ χ))
2	1	nic-isw1 1445	. 2 ⊢ ((χ ⊼ χ) ⊼ ψ)
3		nic-ich.1	. . 3 ⊢ (φ ⊼ (ψ ⊼ ψ))
4	3	nic-imp 1440	. 2 ⊢ (((χ ⊼ χ) ⊼ ψ) ⊼ ((φ ⊼ (χ ⊼ χ)) ⊼ (φ ⊼ (χ ⊼ χ))))
5	2, 4	nic-mp 1436	1 ⊢ (φ ⊼ (χ ⊼ χ))

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-idbl  1451  nic-luk1  1456