Theorem 3eqtr4i

Description: An inference from three chained equalities. (Contributed by NM, 26-May-1993) (Proof shortened by Andrew Salmon, 25-May-2011)

	Ref	Expression
Hypotheses	3eqtr4i.1	$$⊢A=B$$
	3eqtr4i.2	$$⊢C=A$$
	3eqtr4i.3	$$⊢D=B$$
Assertion	3eqtr4i	$$⊢C=D$$

Proof

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