Theorem bitr4id

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

	Ref	Expression
Hypotheses	bitr4id.2	|- ( ps <-> ch )
	bitr4id.1	|- ( ph -> ( th <-> ch ) )
Assertion	bitr4id	|- ( ph -> ( ps <-> th ) )

Proof

Step	Hyp	Ref	Expression
1		bitr4id.2	|- ( ps <-> ch )
2		bitr4id.1	|- ( ph -> ( th <-> ch ) )
3	1	bicomi	|- ( ch <-> ps )
4	2 3	bitr2di	|- ( ph -> ( ps <-> th ) )