Theorem 3eqtrrd

Description: A deduction from three chained equalities. (Contributed by NM, 4-Aug-2006) (Proof shortened by Andrew Salmon, 25-May-2011)

	Ref	Expression
Hypotheses	3eqtrd.1	|- ( ph -> A = B )
	3eqtrd.2	|- ( ph -> B = C )
	3eqtrd.3	|- ( ph -> C = D )
Assertion	3eqtrrd	|- ( ph -> D = A )

Proof

Step	Hyp	Ref	Expression
1		3eqtrd.1	|- ( ph -> A = B )
2		3eqtrd.2	|- ( ph -> B = C )
3		3eqtrd.3	|- ( ph -> C = D )
4	1 2	eqtrd	|- ( ph -> A = C )
5	4 3	eqtr2d	|- ( ph -> D = A )