Theorem 3imtr4i

Description: A mixed syllogism inference, useful for applying a definition to both sides of an implication. (Contributed by NM, 3-Jan-1993)

	Ref	Expression
Hypotheses	3imtr4.1	|- ( ph -> ps )
	3imtr4.2	|- ( ch <-> ph )
	3imtr4.3	|- ( th <-> ps )
Assertion	3imtr4i	|- ( ch -> th )

Proof

Step	Hyp	Ref	Expression
1		3imtr4.1	|- ( ph -> ps )
2		3imtr4.2	|- ( ch <-> ph )
3		3imtr4.3	|- ( th <-> ps )
4	2 1	sylbi	|- ( ch -> ps )
5	4 3	sylibr	|- ( ch -> th )