Theorem sylibrd

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

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

Proof

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