Theorem 3eqtr3g

Description: A chained equality inference, useful for converting from definitions. (Contributed by NM, 15-Nov-1994)

	Ref	Expression
Hypotheses	3eqtr3g.1	|- ( ph -> A = B )
	3eqtr3g.2	|- A = C
	3eqtr3g.3	|- B = D
Assertion	3eqtr3g	|- ( ph -> C = D )

Proof

Step	Hyp	Ref	Expression
1		3eqtr3g.1	|- ( ph -> A = B )
2		3eqtr3g.2	|- A = C
3		3eqtr3g.3	|- B = D
4	2 1	eqtr3id	|- ( ph -> C = B )
5	4 3	eqtrdi	|- ( ph -> C = D )