Theorem 3eqtr4d

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

	Ref	Expression
Hypotheses	3eqtr4d.1	|- ( ph -> A = B )
	3eqtr4d.2	|- ( ph -> C = A )
	3eqtr4d.3	|- ( ph -> D = B )
Assertion	3eqtr4d	|- ( ph -> C = D )

Proof

Step	Hyp	Ref	Expression
1		3eqtr4d.1	|- ( ph -> A = B )
2		3eqtr4d.2	|- ( ph -> C = A )
3		3eqtr4d.3	|- ( ph -> D = B )
4	3 1	eqtr4d	|- ( ph -> D = A )
5	2 4	eqtr4d	|- ( ph -> C = D )