Theorem bitr4di

Description: A syllogism inference from two biconditionals. (Contributed by NM, 12-Mar-1993)

	Ref	Expression
Hypotheses	bitr4di.1	|- ( ph -> ( ps <-> ch ) )
	bitr4di.2	|- ( th <-> ch )
Assertion	bitr4di	|- ( ph -> ( ps <-> th ) )

Proof

Step	Hyp	Ref	Expression
1		bitr4di.1	|- ( ph -> ( ps <-> ch ) )
2		bitr4di.2	|- ( th <-> ch )
3	2	bicomi	|- ( ch <-> th )
4	1 3	bitrdi	|- ( ph -> ( ps <-> th ) )