Theorem 3eqtr4g

Description: A chained equality inference, useful for converting to definitions. (Contributed by NM, 21-Jun-1993)

	Ref	Expression
Hypotheses	3eqtr4g.1	|- ( ph -> A = B )
	3eqtr4g.2	|- C = A
	3eqtr4g.3	|- D = B
Assertion	3eqtr4g	|- ( ph -> C = D )

Proof

Step	Hyp	Ref	Expression
1		3eqtr4g.1	|- ( ph -> A = B )
2		3eqtr4g.2	|- C = A
3		3eqtr4g.3	|- D = B
4	2 1	syl5eq	|- ( ph -> C = B )
5	4 3	eqtr4di	|- ( ph -> C = D )