Theorem 3eqtr4rd

Description: A deduction from three chained equalities. (Contributed by NM, 21-Sep-1995)

	Ref	Expression
Hypotheses	3eqtr4d.1	|- ( ph -> A = B )
	3eqtr4d.2	|- ( ph -> C = A )
	3eqtr4d.3	|- ( ph -> D = B )
Assertion	3eqtr4rd	|- ( ph -> D = C )

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	4 2	eqtr4d	|- ( ph -> D = C )