Theorem 3imtr3i

Description: A mixed syllogism inference, useful for removing a definition from both sides of an implication. (Contributed by NM, 10-Aug-1994)

	Ref	Expression
Hypotheses	3imtr3.1	|- ( ph -> ps )
	3imtr3.2	|- ( ph <-> ch )
	3imtr3.3	|- ( ps <-> th )
Assertion	3imtr3i	|- ( ch -> th )

Proof

Step	Hyp	Ref	Expression
1		3imtr3.1	|- ( ph -> ps )
2		3imtr3.2	|- ( ph <-> ch )
3		3imtr3.3	|- ( ps <-> th )
4	2 1	sylbir	|- ( ch -> ps )
5	4 3	sylib	|- ( ch -> th )