Theorem syli

Description: Syllogism inference with common nested antecedent. (Contributed by NM, 4-Nov-2004)

	Ref	Expression
Hypotheses	syli.1	|- ( ps -> ( ph -> ch ) )
	syli.2	|- ( ch -> ( ph -> th ) )
Assertion	syli	|- ( ps -> ( ph -> th ) )

Proof

Step	Hyp	Ref	Expression
1		syli.1	|- ( ps -> ( ph -> ch ) )
2		syli.2	|- ( ch -> ( ph -> th ) )
3	2	com12	|- ( ph -> ( ch -> th ) )
4	1 3	sylcom	|- ( ps -> ( ph -> th ) )