Theorem bitr3di

Description: A syllogism inference from two biconditionals. (Contributed by NM, 25-Nov-1994)

	Ref	Expression
Hypotheses	bitr3di.1	|- ( ph -> ( ps <-> ch ) )
	bitr3di.2	|- ( ps <-> th )
Assertion	bitr3di	|- ( ph -> ( ch <-> th ) )

Proof

Step	Hyp	Ref	Expression
1		bitr3di.1	|- ( ph -> ( ps <-> ch ) )
2		bitr3di.2	|- ( ps <-> th )
3	2	bicomi	|- ( th <-> ps )
4	3 1	bitr2id	|- ( ph -> ( ch <-> th ) )