Theorem 3eqtr2i

Description: An inference from three chained equalities. (Contributed by NM, 3-Aug-2006)

	Ref	Expression
Hypotheses	3eqtr2i.1	$$⊢A=B$$
	3eqtr2i.2	$$⊢C=B$$
	3eqtr2i.3	$$⊢C=D$$
Assertion	3eqtr2i	$$⊢A=D$$

Proof

Step	Hyp	Ref	Expression
1		3eqtr2i.1	$$⊢A=B$$
2		3eqtr2i.2	$$⊢C=B$$
3		3eqtr2i.3	$$⊢C=D$$
4	1 2	eqtr4i	$$⊢A=C$$
5	4 3	eqtri	$$⊢A=D$$