Theorem 3eqtr3rd

Description: A deduction from three chained equalities. (Contributed by NM, 14-Jan-2006)

	Ref	Expression
Hypotheses	3eqtr3d.1	|- ( ph -> A = B )
	3eqtr3d.2	|- ( ph -> A = C )
	3eqtr3d.3	|- ( ph -> B = D )
Assertion	3eqtr3rd	|- ( ph -> D = C )

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	3 4	eqtr3d	|- ( ph -> D = C )