Theorem 3eqtr4a

Description: A chained equality inference, useful for converting to definitions. (Contributed by NM, 2-Feb-2007) (Proof shortened by Andrew Salmon, 25-May-2011)

	Ref	Expression
Hypotheses	3eqtr4a.1	|- A = B
	3eqtr4a.2	|- ( ph -> C = A )
	3eqtr4a.3	|- ( ph -> D = B )
Assertion	3eqtr4a	|- ( ph -> C = D )

Proof

Step	Hyp	Ref	Expression
1		3eqtr4a.1	|- A = B
2		3eqtr4a.2	|- ( ph -> C = A )
3		3eqtr4a.3	|- ( ph -> D = B )
4	2 1	eqtrdi	|- ( ph -> C = B )
5	4 3	eqtr4d	|- ( ph -> C = D )