Theorem sylbid

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

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

Proof

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