Theorem syl6mpi

Description: A syllogism inference. (Contributed by Alan Sare, 8-Jul-2011) (Proof shortened by Wolf Lammen, 13-Sep-2012)

	Ref	Expression
Hypotheses	syl6mpi.1	|- ( ph -> ( ps -> ch ) )
	syl6mpi.2	|- th
	syl6mpi.3	|- ( ch -> ( th -> ta ) )
Assertion	syl6mpi	|- ( ph -> ( ps -> ta ) )

Proof

Step	Hyp	Ref	Expression
1		syl6mpi.1	|- ( ph -> ( ps -> ch ) )
2		syl6mpi.2	|- th
3		syl6mpi.3	|- ( ch -> ( th -> ta ) )
4	2 3	mpi	|- ( ch -> ta )
5	1 4	syl6	|- ( ph -> ( ps -> ta ) )