Theorem 3eqtr3a

Description: A chained equality inference, useful for converting from definitions. (Contributed by Mario Carneiro, 6-Nov-2015)

	Ref	Expression
Hypotheses	3eqtr3a.1	|- A = B
	3eqtr3a.2	|- ( ph -> A = C )
	3eqtr3a.3	|- ( ph -> B = D )
Assertion	3eqtr3a	|- ( ph -> C = D )

Proof

Step	Hyp	Ref	Expression
1		3eqtr3a.1	|- A = B
2		3eqtr3a.2	|- ( ph -> A = C )
3		3eqtr3a.3	|- ( ph -> B = D )
4	1 3	syl5eq	|- ( ph -> A = D )
5	2 4	eqtr3d	|- ( ph -> C = D )