Theorem 3eqtr3i

Description: An inference from three chained equalities. (Contributed by NM, 6-May-1994) (Proof shortened by Andrew Salmon, 25-May-2011)

	Ref	Expression
Hypotheses	3eqtr3i.1	$$⊢A=B$$
	3eqtr3i.2	$$⊢A=C$$
	3eqtr3i.3	$$⊢B=D$$
Assertion	3eqtr3i	$$⊢C=D$$

Proof

Step	Hyp	Ref	Expression
1		3eqtr3i.1	$$⊢A=B$$
2		3eqtr3i.2	$$⊢A=C$$
3		3eqtr3i.3	$$⊢B=D$$
4	1 2	eqtr3i	$$⊢B=C$$
5	4 3	eqtr3i	$$⊢C=D$$