Theorem sylibd

Description: A syllogism deduction. (Contributed by NM, 3-Aug-1994)

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

Proof

Step	Hyp	Ref	Expression
1		sylibd.1	|- ( ph -> ( ps -> ch ) )
2		sylibd.2	|- ( ph -> ( ch <-> th ) )
3	2	biimpd	|- ( ph -> ( ch -> th ) )
4	1 3	syld	|- ( ph -> ( ps -> th ) )