Theorem biimtrdi

Description: A mixed syllogism inference. (Contributed by NM, 2-Jan-1994)

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

Proof

Step	Hyp	Ref	Expression
1		biimtrdi.1	|- ( ph -> ( ps <-> ch ) )
2		biimtrdi.2	|- ( ch -> th )
3	1	biimpd	|- ( ph -> ( ps -> ch ) )
4	3 2	syl6	|- ( ph -> ( ps -> th ) )