Theorem 3eqtr3d

Description: A deduction from three chained equalities. (Contributed by NM, 4-Aug-1995) (Proof shortened by Andrew Salmon, 25-May-2011)

	Ref	Expression
Hypotheses	3eqtr3d.1	|- ( ph -> A = B )
	3eqtr3d.2	|- ( ph -> A = C )
	3eqtr3d.3	|- ( ph -> B = D )
Assertion	3eqtr3d	|- ( ph -> C = D )

Proof

Step	Hyp	Ref	Expression
1		3eqtr3d.1	|- ( ph -> A = B )
2		3eqtr3d.2	|- ( ph -> A = C )
3		3eqtr3d.3	|- ( ph -> B = D )
4	1 2	eqtr3d	|- ( ph -> B = C )
5	4 3	eqtr3d	|- ( ph -> C = D )