Theorem nic-ich

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

	Ref	Expression
Hypotheses	nic-ich.1	|- ( ph -/\ ( ps -/\ ps ) )
	nic-ich.2	|- ( ps -/\ ( ch -/\ ch ) )
Assertion	nic-ich	|- ( ph -/\ ( ch -/\ ch ) )

Proof

Step	Hyp	Ref	Expression
1		nic-ich.1	|- ( ph -/\ ( ps -/\ ps ) )
2		nic-ich.2	|- ( ps -/\ ( ch -/\ ch ) )
3	2	nic-isw1	|- ( ( ch -/\ ch ) -/\ ps )
4	1	nic-imp	|- ( ( ( ch -/\ ch ) -/\ ps ) -/\ ( ( ph -/\ ( ch -/\ ch ) ) -/\ ( ph -/\ ( ch -/\ ch ) ) ) )
5	3 4	nic-mp	|- ( ph -/\ ( ch -/\ ch ) )