Theorem bitrid

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

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

Proof

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