Theorem syl6ci

Description: A syllogism inference combined with contraction. (Contributed by Alan Sare, 18-Mar-2012)

	Ref	Expression
Hypotheses	syl6ci.1	|- ( ph -> ( ps -> ch ) )
	syl6ci.2	|- ( ph -> th )
	syl6ci.3	|- ( ch -> ( th -> ta ) )
Assertion	syl6ci	|- ( ph -> ( ps -> ta ) )

Proof

Step	Hyp	Ref	Expression
1		syl6ci.1	|- ( ph -> ( ps -> ch ) )
2		syl6ci.2	|- ( ph -> th )
3		syl6ci.3	|- ( ch -> ( th -> ta ) )
4	2	a1d	|- ( ph -> ( ps -> th ) )
5	1 4 3	syl6c	|- ( ph -> ( ps -> ta ) )