Theorem 3eqtrd

Description: A deduction from three chained equalities. (Contributed by NM, 29-Oct-1995)

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

Proof

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