Theorem bitrdi

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

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

Proof

Step	Hyp	Ref	Expression
1		bitrdi.1	|- ( ph -> ( ps <-> ch ) )
2		bitrdi.2	|- ( ch <-> th )
3	2	a1i	|- ( ph -> ( ch <-> th ) )
4	1 3	bitrd	|- ( ph -> ( ps <-> th ) )