Theorem 3eqtr2d

Description: A deduction from three chained equalities. (Contributed by NM, 4-Aug-2006)

	Ref	Expression
Hypotheses	3eqtr2d.1	|- ( ph -> A = B )
	3eqtr2d.2	|- ( ph -> C = B )
	3eqtr2d.3	|- ( ph -> C = D )
Assertion	3eqtr2d	|- ( ph -> A = D )

Proof

Step	Hyp	Ref	Expression
1		3eqtr2d.1	|- ( ph -> A = B )
2		3eqtr2d.2	|- ( ph -> C = B )
3		3eqtr2d.3	|- ( ph -> C = D )
4	1 2	eqtr4d	|- ( ph -> A = C )
5	4 3	eqtrd	|- ( ph -> A = D )