Theorem sylsyld

Description: A double syllogism inference. (Contributed by Alan Sare, 20-Apr-2011)

	Ref	Expression
Hypotheses	sylsyld.1	|- ( ph -> ps )
	sylsyld.2	|- ( ph -> ( ch -> th ) )
	sylsyld.3	|- ( ps -> ( th -> ta ) )
Assertion	sylsyld	|- ( ph -> ( ch -> ta ) )

Proof

Step	Hyp	Ref	Expression
1		sylsyld.1	|- ( ph -> ps )
2		sylsyld.2	|- ( ph -> ( ch -> th ) )
3		sylsyld.3	|- ( ps -> ( th -> ta ) )
4	1 3	syl	|- ( ph -> ( th -> ta ) )
5	2 4	syld	|- ( ph -> ( ch -> ta ) )